{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4b5849aa",
   "metadata": {},
   "source": [
    "# Connectivity Constraint "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "890e58ab",
   "metadata": {},
   "source": [
    "For manufacturability, it is often necessary to impose connectivity constraint during topological optimization, so that all solid pixels are connected to one side (e.g. the supporting substrate). Meep adjoint supports this feature and it is illustrated in this tutorial. Please also note that the connectivity constraint is independent from the rest of Meep, and may be used independently and separately.\n",
    "\n",
    "The basic underlying idea is to solve for an auxilary artificial temperature field. For connected structure, heat can freely flow out through the supporing layer, so the temperature in the region should be low overall; on the other hand, for disconnected structure, heat will be trapped in islands, leading to high temperature in some area. Reference: Li, Q., Chen, W., Liu, S. et al. \"Structural topology optimization considering connectivity constraint\". Struct Multidisc Optim 54, 971–984 (2016). https://doi.org/10.1007/s00158-016-1459-5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a6964ee3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using MPI version 3.1, 1 processes\n"
     ]
    }
   ],
   "source": [
    "import meep as mp\n",
    "from meep import Animate2D\n",
    "import meep.adjoint as mpa\n",
    "import numpy as np\n",
    "from autograd import numpy as npa\n",
    "from autograd import tensor_jacobian_product, grad\n",
    "import nlopt\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.patches import Circle\n",
    "from scipy import special, signal\n",
    "\n",
    "mp.verbosity(0)\n",
    "Si = mp.Medium(index=3.4)\n",
    "Air = mp.Medium(index=1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3dc1f9ab",
   "metadata": {},
   "source": [
    "# I. How the Connectivity Constraint Works"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4210a705",
   "metadata": {},
   "source": [
    "Given (filtered and projected) design variable `v` with size `(nz, ny, nx)`, `mpa.constraint_connectivity(v, nx, ny, nz)` computes and simultaneously outputs the constraint value (negative for connected structure, positive for disconnected structure) and the gradient of the constraint with respect to `v`. Additional chain rule needs to be applied for gradient with repect to the unprojected and unfiltered design variables.\n",
    "\n",
    "The temperature field is also returned for debug and reference, but it can be ignored when using the constraint.\n",
    "#### IMPORTANT: The solver will reshape input `v` via `np.reshape(v, (nz, ny, nx))`. For 2D structure, please specify `ny=1`. The solver assumes the last index of the 0-axis of the array (bottom side of the image from plt.imshow) is where the structure should be connected. So the user must first rotate the structure properly to match this condition; the gradient must also be post-processed and rotated so that the gradient corresponds correctly.\n",
    "\n",
    "There are three important hyperparameter, `p`, `cond_s`, and `thresh`. It is advised to check and tune them for each individual problem setup so that the constraint behaves as expected. A tall design region might require larger `cond_s` and `thresh`, as the heat is more difficult to flow out. On the other hand, there are many good combinations, and a reasonably conservative `thresh` might be all one needs to tune. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d86eeb17",
   "metadata": {},
   "source": [
    "### disconnected structure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7299cb1d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fb2bdf38f10>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nz, ny, nx = 100, 1, 50\n",
    "v = np.zeros((nz,ny,nx))\n",
    "v[30:65,:,20:30]=1\n",
    "v[70:,:,20:30]=1\n",
    "plt.imshow(v[:,0,:])\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ad6e653",
   "metadata": {},
   "source": [
    "The structure above has one part that is connected to the bottom, while the other part is floating above and is disconnected. We can see overall has a positive constraint value of around 24"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8e8f0e8d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.234376324325485"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T, f, df_dv = mpa.constraint_connectivity(v, nx, ny, nz, p=3, cond_s=1e4, thresh=50)\n",
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "df183225",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fb2bf493430>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(T.reshape(nz, nx))\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7367fc3",
   "metadata": {},
   "source": [
    "The temperature in the region is plotted above. As we can see, only the top disconnected part is heated up, while the bottom connected part is cooled down. We also plotted the gradient below, which has large negative values between the two components, indicating strong tendency to connect the structure in order to lower the temperature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fb8073ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fb2be29f9d0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(df_dv.reshape(nz, nx))\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b886600",
   "metadata": {},
   "source": [
    "### connected structure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ee852785",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fb2be170160>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "v[30:,:,40]=1\n",
    "v[40,:,30:40]=1\n",
    "plt.imshow(v[:,0,:])\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6fd7737b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.2505643580057533"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T, f, df_dv = mpa.constraint_connectivity(v, nx, ny, nz, p=3, cond_s=1e4, thresh=50)\n",
    "f"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c02f16f7",
   "metadata": {},
   "source": [
    "If we connect the structure so that all solid pixel is path-connected to the bottom, we can see that the constraint value becomes negative, and the tempeature is low overall as heat is leaked through the bottom side. The gradient values are relatively small in generall as well, indicating no more change is needed to connect the structure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "50dd1f7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fb2bf527340>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(T.reshape(nz, nx))\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "df47301c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fb2be589b50>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(df_dv.reshape(nz, nx))\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "119e6ba2",
   "metadata": {},
   "source": [
    "# II. Optimization Example\n",
    "\n",
    "We further illustrates the constraint with the following topological optimization example. A simple metalens sitting on a substrate is designed to focus light. Length-scale and connectivity constraints are both imposed to ensure manufactuability. Length-scale is imposed so that components are connected by more than a narrow path of a few pixels, and eliminate small islands that don't signicantly violates the connectivity constraint.\n",
    "\n",
    "In this example, we not only enforce solid pixels to connect to the substrate, we also enforce the void pixels to connect to the air above. Therefore, the structure has no holes and can be easily cleaned with alcohol."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e838e472",
   "metadata": {},
   "outputs": [],
   "source": [
    "pad = 0.1\n",
    "design_region_width0 = 8\n",
    "design_region_height0 = 2\n",
    "design_region_width = design_region_width0 + 2*pad\n",
    "design_region_height = design_region_height0 + 2*pad\n",
    "\n",
    "pml_size = 1.0\n",
    "\n",
    "resolution = 30\n",
    "\n",
    "Sx = 2 * pml_size + design_region_width\n",
    "Sy = 2 * pml_size + design_region_height + 3\n",
    "cell_size = mp.Vector3(Sx, Sy)\n",
    "\n",
    "nf = 1\n",
    "frequencies = np.array([1 / 1.55])\n",
    "\n",
    "minimum_length = 0.15  \n",
    "eta_i = 0.5\n",
    "eta_e = 0.75\n",
    "eta_d = 1 - eta_e\n",
    "filter_radius = mpa.get_conic_radius_from_eta_e(minimum_length, eta_e)\n",
    "design_region_resolution = int(resolution)\n",
    "\n",
    "pml_layers = [mp.PML(pml_size)]\n",
    "\n",
    "\n",
    "\n",
    "fcen = 1 / 1.55\n",
    "width = 0.1\n",
    "fwidth = width * fcen\n",
    "source_center = [0, -(design_region_height / 2 + 1), 0]\n",
    "source_size = mp.Vector3(design_region_width, 0, 0)\n",
    "src = mp.GaussianSource(frequency=fcen, fwidth=fwidth)\n",
    "source = [mp.Source(src, component=mp.Ez, size=source_size, center=source_center)]\n",
    "\n",
    "Nx = round(design_region_resolution * design_region_width)\n",
    "Ny = round(design_region_resolution * design_region_height)\n",
    "\n",
    "design_variables = mp.MaterialGrid(mp.Vector3(Nx, Ny), Air, Si,damping=0.2*6.28*fcen)\n",
    "design_region = mpa.DesignRegion(\n",
    "    design_variables,\n",
    "    volume=mp.Volume(\n",
    "        center=mp.Vector3(),\n",
    "        size=mp.Vector3(design_region_width, design_region_height, 0),\n",
    "    ),\n",
    ")\n",
    "\n",
    "\n",
    "# Padding and masking the design region to ensure geometric constraints on the boundaries.\n",
    "mask = pad\n",
    "x_g = np.linspace(-design_region_width / 2, design_region_width / 2, Nx)\n",
    "y_g = np.linspace(-design_region_height / 2, design_region_height / 2, Ny)\n",
    "X_g, Y_g = np.meshgrid(x_g, y_g, sparse=True, indexing=\"ij\")\n",
    "left_mask = (X_g <= -(design_region_width/2-mask)) & (np.abs(Y_g) <= design_region_height / 2)\n",
    "right_mask = (X_g >= design_region_width/2-mask) & (np.abs(Y_g) <= design_region_height / 2)\n",
    "top_mask = (Y_g >= design_region_height/2-mask) & (np.abs(X_g) <= design_region_width / 2)\n",
    "bottom_mask = (Y_g <= -(design_region_height/2-mask)) & (np.abs(X_g) <= design_region_width / 2)\n",
    "Air_mask = left_mask | top_mask | right_mask\n",
    "\n",
    "def mapping(x,eta,beta):                                                                                                                                                       \n",
    "    xc = npa.where(bottom_mask.flatten(),1,npa.where(Air_mask.flatten(),0,x))\n",
    "    xc = npa.reshape(xc, (Nx, Ny))                                                                                                                                        \n",
    "\n",
    "    # filter                                                                                                                                                               \n",
    "    filtered_field = mpa.conic_filter(xc,filter_radius,design_region_width,design_region_height, design_region_resolution)                                                                                                                                 \n",
    "    return filtered_field.flatten()\n",
    "\n",
    "\n",
    "# ``mapping_s`` and ``mapping_v`` are very important functions: they pre-process the design variables by masking, \n",
    "# filtering, projecting, and rotating to the proper orientation. The mapping function above is for the Maxwell solves, \n",
    "# and has no projection because that is taken care of as part of meep routine, using beta defined in the design variable. \n",
    "# On the other hand, for connectivity constraint, projection must be separatly specified. Afterwards, \n",
    "# ``rot90`` in ``mapping_s`` would rotate the meep design variables properly for the constraint, \n",
    "# so that connectivity of solid to the bottom is enforced. Similarly, in ``mapping_v``,\n",
    "# ``1 - npa.rot90(projected_field,3)`` are for the void pixels to connect to the air above.\n",
    "# Packing the preprocessing functions this way allows for easy post-processsing of the gradients with chain-rule.\n",
    "\n",
    "def mapping_s(x,eta,beta):\n",
    "    # filter\n",
    "    xc = npa.where(bottom_mask.flatten(),1,npa.where(Air_mask.flatten(),0,x))\n",
    "    xc = npa.reshape(xc, (Nx, Ny))\n",
    "    filtered_field = mpa.conic_filter(x,filter_radius,design_region_width, design_region_height, design_region_resolution)\n",
    "    # projection                                                                                                                                                          \n",
    "    projected_field = mpa.tanh_projection(filtered_field,beta,eta)\n",
    "\n",
    "    rot_field = npa.rot90(projected_field)\n",
    "    return rot_field.flatten()\n",
    "\n",
    "def mapping_v(x,eta,beta):\n",
    "    # filter      \n",
    "    xc = npa.where(bottom_mask.flatten(),1,npa.where(Air_mask.flatten(),0,x))\n",
    "    xc = npa.reshape(xc, (Nx, Ny))\n",
    "    filtered_field = mpa.conic_filter(x,filter_radius,design_region_width, design_region_height, design_region_resolution)\n",
    "    # projection                                                                                                                                                          \n",
    "    projected_field = mpa.tanh_projection(filtered_field,beta,eta)\n",
    "\n",
    "    rot_field = 1 - npa.rot90(projected_field, 3)\n",
    "    return rot_field.flatten()\n",
    "\n",
    "\n",
    "geometry = [\n",
    "    mp.Block(center=design_region.center, size=design_region.size, material=design_variables),\n",
    "    mp.Block(center=mp.Vector3(0, -design_region_height0 / 2 - 0.25), size=mp.Vector3(design_region_width, 0.5), material=Si),\n",
    "]\n",
    "sim = mp.Simulation(\n",
    "    cell_size=cell_size,\n",
    "    boundary_layers=pml_layers,\n",
    "    geometry=geometry,\n",
    "    sources=source,\n",
    "    default_material=Air,\n",
    "    resolution=resolution,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "dbaa2395",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "far_x = [mp.Vector3(0, 5, 0)]\n",
    "NearRegions = [\n",
    "    mp.Near2FarRegion(\n",
    "        center=mp.Vector3(0, design_region_height / 2 + 0.5),\n",
    "        size=mp.Vector3(design_region_width, 0),\n",
    "        weight=+1,\n",
    "    )\n",
    "]\n",
    "FarFields = mpa.Near2FarFields(sim, NearRegions, far_x)\n",
    "ob_list = [FarFields]\n",
    "\n",
    "def J(FF):\n",
    "    return npa.abs(FF[0, 0, 2]) ** 2\n",
    "\n",
    "opt = mpa.OptimizationProblem(\n",
    "    simulation=sim,\n",
    "    objective_functions=[J],\n",
    "    objective_arguments=ob_list,\n",
    "    design_regions=[design_region],\n",
    "    frequencies=frequencies,\n",
    "    maximum_run_time=500,\n",
    ")\n",
    "opt.plot2D(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "229cfe3f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current iteration: 1\n",
      "Starting forward run...\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3ebed0792ef644a0b02d536ad6da6741",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Current iteration: 2\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Current iteration: 3\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Current iteration: 4\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Current iteration: 5\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Current iteration: 6\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Current iteration: 7\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Current iteration: 8\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Current iteration: 9\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
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    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.9/site-packages/meep/geom.py:582: UserWarning: The weights parameter of MaterialGrid must be in the range [0,1].\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
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   ],
   "source": [
    "evaluation_history = []\n",
    "connectivity_s_history = []\n",
    "connectivity_v_history = []\n",
    "geom_s_history = []\n",
    "geom_v_history = []\n",
    "cur_iter = [0]\n",
    "\n",
    "def f(v, gradient, beta):\n",
    "    print(\"Current iteration: {}\".format(cur_iter[0] + 1))\n",
    "\n",
    "    f0, dJ_du = opt([mapping(v, eta_i, beta)])  # compute objective and gradient\n",
    "\n",
    "    if gradient.size > 0:\n",
    "        gradient[:] = tensor_jacobian_product(mapping, 0)(\n",
    "            v, eta_i, beta, dJ_du\n",
    "        )  # backprop\n",
    "\n",
    "    evaluation_history.append(np.real(f0))\n",
    "    cur_iter[0] = cur_iter[0] + 1\n",
    "\n",
    "    return np.real(f0)\n",
    "\n",
    "def connect_s(x,gradient,eta,beta):                                                                                                                                   \n",
    "\n",
    "    v0 = x[:] # design parameters                                                                                                                                        \n",
    "    v = mapping_s(v0,eta_i,beta)#pre-process with mapping_s\n",
    "    _, f0, dJ_du = mpa.constraint_connectivity(v, Nx, 1, Ny, p=3, cond_s=500, thresh=30)\n",
    "    dJ_du = np.squeeze(dJ_du)                                                                                                                        \n",
    "    my_grad = tensor_jacobian_product(mapping_s,0)(v0,eta,beta,dJ_du)\n",
    "    gradient[:] = my_grad.flatten()\n",
    "\n",
    "    connectivity_s_history.append(f0)\n",
    "    return f0\n",
    "\n",
    "def connect_v(x,gradient,eta,beta):                                                                                                                                   \n",
    "\n",
    "    v0 = x[:] # design parameters                                                                                                                                        \n",
    "    v = mapping_v(v0,eta_i,beta)#pre-process with mapping_v\n",
    "    _, f0, dJ_du = mpa.constraint_connectivity(v, Nx, 1, Ny, p=3, cond_s=500, thresh=30)\n",
    "    dJ_du = np.squeeze(dJ_du)                                                                                                                        \n",
    "    my_grad = tensor_jacobian_product(mapping_v,0)(v0,eta,beta,dJ_du)\n",
    "    gradient[:] = my_grad.flatten()\n",
    "\n",
    "    connectivity_v_history.append(f0)\n",
    "    return f0\n",
    "\n",
    "def geom_s(x,gradient,eta,beta):\n",
    "                                                                                                                                            \n",
    "    threshf = lambda v: mpa.tanh_projection(v,beta,eta)\n",
    "    filterf = lambda v: mpa.conic_filter(v.reshape(Nx, Ny),filter_radius,design_region_width,design_region_height,design_region_resolution)\n",
    "    v = x[:]\n",
    "\n",
    "    v = npa.where(bottom_mask.flatten(),1,npa.where(Air_mask.flatten(),0,v))\n",
    "\n",
    "    v_c=(filter_radius/resolution)**4                                                                                                                                  \n",
    "    g_s = mpa.constraint_solid(v,v_c,eta_e,filterf,threshf,1)                                                                       \n",
    "    g_s_grad = grad(mpa.constraint_solid,0)(v,v_c,eta_e,filterf,threshf,1)                                                                                                                                                                                                                 \n",
    "    gradient[:]  = npa.where(bottom_mask.flatten() | Air_mask.flatten(),0,g_s_grad)\n",
    "    geom_s_history.append(g_s)\n",
    "    return float(g_s)-1e-3\n",
    "\n",
    "def geom_v(x,gradient,eta,beta):\n",
    "                                                                                                                                            \n",
    "    threshf = lambda v: mpa.tanh_projection(v,beta,eta)\n",
    "    filterf = lambda v: mpa.conic_filter(v.reshape(Nx, Ny),filter_radius,design_region_width,design_region_height,design_region_resolution)\n",
    "    v = x[:]\n",
    "\n",
    "    v = npa.where(bottom_mask.flatten(),1,npa.where(Air_mask.flatten(),0,v))\n",
    "    v_c=(filter_radius/resolution)**4                                                                                                                                   \n",
    "    g_v = mpa.constraint_void(v,v_c,eta_d,filterf,threshf,1)                                                                      \n",
    "    g_v_grad = grad(mpa.constraint_void,0)(v,v_c,eta_d,filterf,threshf,1)                                                                                                                                                                                                                \n",
    "    gradient[:]  = npa.where(bottom_mask.flatten() | Air_mask.flatten(),0,g_v_grad)\n",
    "    geom_v_history.append(g_v)\n",
    "    return float(g_v)-1e-3\n",
    "\n",
    "\n",
    "%matplotlib ipympl\n",
    "# Create the animation\n",
    "animate = Animate2D(\n",
    "    fields=None,\n",
    "    realtime=True,\n",
    "    eps_parameters={'contour': False, 'alpha': 1, 'frequency': 1/1.55},\n",
    "    plot_sources_flag=False,\n",
    "    plot_monitors_flag=False,\n",
    "    plot_boundaries_flag=False,\n",
    "    update_epsilon=True,  # required for the geometry to update dynamically\n",
    "    nb=True         # required if running in a Jupyter notebook\n",
    ")\n",
    "# This will trigger the animation at the end of each simulation\n",
    "opt.step_funcs=[mp.at_end(animate)]\n",
    "\n",
    "\n",
    "algorithm = nlopt.LD_MMA\n",
    "n = Nx * Ny  # number of parameters\n",
    "\n",
    "# Initial guess\n",
    "x = np.ones((n,)) * 0.5\n",
    "\n",
    "# lower and upper bounds\n",
    "lb = np.zeros((Nx * Ny,))\n",
    "ub = np.ones((Nx * Ny,))\n",
    "\n",
    "\n",
    "# Length-scale constraints are introduced in the last beta, as they requires almost binaried structures.\n",
    "# Connectivity constraints are less well-defined when there are too many grey scale pixels, but they can \n",
    "# be introduced earlier to guide the evolution in the right direction before the structure gets too disconnected.\n",
    "\n",
    "cur_beta = 8\n",
    "beta_scale = 2\n",
    "num_betas = 3\n",
    "update_factor = 50\n",
    "ftol = 1e-5\n",
    "for iters in range(num_betas):\n",
    "    design_variables.beta = cur_beta\n",
    "    solver = nlopt.opt(algorithm, n)\n",
    "    solver.set_lower_bounds(lb)\n",
    "    solver.set_upper_bounds(ub)\n",
    "    solver.set_max_objective(lambda a, g: f(a, g, cur_beta))\n",
    "    if cur_beta >= 16:\n",
    "        solver.add_inequality_constraint(lambda x,g: connect_s(x,g,eta_i, cur_beta), 1e-3)\n",
    "        solver.add_inequality_constraint(lambda x,g: connect_v(x,g,eta_i, cur_beta), 1e-3)\n",
    "        solver.add_inequality_constraint(lambda x,g: geom_s(x,g,eta_i, cur_beta), 1e-3)\n",
    "        solver.add_inequality_constraint(lambda x,g: geom_v(x,g,eta_i, cur_beta), 1e-3)\n",
    "    solver.set_maxeval(update_factor)\n",
    "    solver.set_ftol_rel(ftol)\n",
    "    x[:] = solver.optimize(x)\n",
    "    cur_beta = cur_beta * beta_scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a5da86a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img3547b06d863445b79306663ccf33e1a6\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider3547b06d863445b79306663ccf33e1a6\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim3547b06d863445b79306663ccf33e1a6.set_frame(parseInt(this.value));\">\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim3547b06d863445b79306663ccf33e1a6.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim3547b06d863445b79306663ccf33e1a6.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim3547b06d863445b79306663ccf33e1a6.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim3547b06d863445b79306663ccf33e1a6.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim3547b06d863445b79306663ccf33e1a6.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim3547b06d863445b79306663ccf33e1a6.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim3547b06d863445b79306663ccf33e1a6.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim3547b06d863445b79306663ccf33e1a6.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim3547b06d863445b79306663ccf33e1a6.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select3547b06d863445b79306663ccf33e1a6\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_3547b06d863445b79306663ccf33e1a6\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_3547b06d863445b79306663ccf33e1a6\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_3547b06d863445b79306663ccf33e1a6\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_3547b06d863445b79306663ccf33e1a6\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_3547b06d863445b79306663ccf33e1a6\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_3547b06d863445b79306663ccf33e1a6\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img3547b06d863445b79306663ccf33e1a6\";\n",
       "    var slider_id = \"_anim_slider3547b06d863445b79306663ccf33e1a6\";\n",
       "    var loop_select_id = \"_anim_loop_select3547b06d863445b79306663ccf33e1a6\";\n",
       "    var frames = new Array(300);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoAAAAHgCAYAAAA10dzkAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
       "bGliIHZlcnNpb24zLjYuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/P9b71AAAACXBIWXMAAA9h\\\n",
       "AAAPYQGoP6dpAAAtTklEQVR4nO3de5CdZX0H8N/Z3WRzIbsIDVAmG7nYsaBCWm5GHQ2aCkynlTql\\\n",
       "/mHLZRjG0sDIxLaQXqDM6MQZmNYpUGAYBKeV0RZBaltUqiVMR5HIRRENnYhATASSYHZDSDbJ7vYP\\\n",
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       "gMQIgAAAiREAAQASIwACACRGAAQASIwACACQGAEQACAxAiAAQGIEQACAxAiAAACJEQABABIjAAIA\\\n",
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       "CIAAAACGIQACAAAYhgAIAABgmP8PeLv2Bk7RWaQAAAAASUVORK5CYII=\\\n",
       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        anim3547b06d863445b79306663ccf33e1a6 = new Animation(frames, img_id, slider_id, 200,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<meep.visualization.JS_Animation at 0x7fb2bdfe86a0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "animate.to_jshtml(fps=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1b4a1358",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb2bf3ad520>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "plt.plot(connectivity_s_history, label=\"connect solid\")\n",
    "plt.plot(connectivity_v_history, label=\"connect void\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "807663b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb2c161bdf0>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "plt.plot(evaluation_history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2fa052c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5e11667180654900b55b457cc5730538",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FloatProgress(value=0.0, description='0% done ', max=500.0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot: xlabel='X', ylabel='Y'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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EyhlkNfGbwVQIU003ghB+E4C/sSRDpt7GcToHnWCTDi7JMUJRNoCYDTga61AIlBLkwgcTYwqKll61ikFG3UThrxB9D7EU8PEcE2ILdQhsGudVsdpGY9h/fzwsjXUIKagsWCymFlgpqKUgTToonfrgX52AyhD1BJHV2LKAqpi9D2txdeVdvkIiZIGsBEnaCQZ3VImmKlYBqADkqGIV0RsXVDJq/+S19a5bhPC2UfjeP+6xf02CIwLjh3annQsZIs0+FSMG+IDmdI7u2tpxRYmhBSRKkAa7IxEOUU7AlFBXXjrFqVc6BBUkQkpIUpAaqzJckjWSog2K0k7TVGIUPg6tJCKkv8TAWKYESYi6i3qCqCvvGatLhK286zI6Adx0AwmlQfvotZPeCeB0jtMJTudU0Z1tojMCaicaoMT70k7436VDS0FlBYmUpFkflXaQ5RhnMkRVIFQCWe6liJ1N8yC42l1d+furBEnaBek9UQ5vb+RXAIhwAowNXi6BDLKgCmkrWiqPs6vQhj5y4tjzvuclBYcQYhH4BeDl+N32l51zH32+z0Vg/NK7398Aw0+P8EE2ZiPfAJWlkRa1m6oTbWAkwW2bakEaost+QxZTse2maRRCJ97eE2Ia3FMpTqczoChq5wF5mQh8MxeSWVVGSTIlyNrqXDlEVGPcZIgb7eAmo6mHLDgC2mqY0D5qTdZB5l1kp4fIe8i8h0u7yKRLknYwWvt7bKt40KhhMRcqBkBL4bz71wgyJcmyPsoZhA7qVl2CKoOa45pUDwch1dn416SCuiDRORaBc8LvyNoHAsHOAMRZRy2Fj5V4Z3BY26mU0sJ7w9rhPhEyf3fvn+cbL7Xk+GngQ865Py+ESIHu831gBhhH7p3J+Y9RUBNO46qlNhnnF7sO+ixcCoxUCZJwSqdKemCY0p/UJqhQzqtRoHA+vdWfykp7QESbwgmqoE+3g4yT2l5i52jpv9O7Nr2OnytBrgWyGnuXcTHADbcwgy3sYBM72KIaTai2x9STCaaosbXxpzUgpERqhco0utch6eWkcz1Ep4/sLyLnl5CdOUTdR2R9ZNLx26mWGGe9hKh4bv1fSwoDWS3JtCRJet7tW01CsLAImQLVrkicj4148Hipm6h0Kj1UlMuzAPEfddSAkBblvJu+sm6atauEX1cuDfhJaLKbf+nd7+c9f/cdz7nXXjJwCCEWgHuBHwRwzpVA+Xyf+6ErlG5GYNhggEXdOkqOOtgZrQynmXyeVInpPylIFciQioKtmsCSV9kIqpQCKT0gVOJBgfJR99oyMR4Uw7JmUtsgLaY1DhKfi5Vrhbb+1NQy2DkRGJNtD4ydDczWGnZ7g2Jjm3JrQLkzoh5OKIclpjTURd1kdQgFOtOoVJH2UnQvJ53rki3PkU5GuHKMWlhFzNnGkE+TTpAYIgTj/Gac1Oay950on8DYSzUT450XU5AYRJXMgiTaRUIGgBgQFRiJFJJUaS89ZoYHSM1U/TT4QKIKalUdwSEEIvhplbgUHO2D9WoqKF9KyXEDcAH4JSHEq4BPA3/DOTdsv0kI8T8C/yMACzQPFicDCPUDfnhg+IxWY6deGZ9dG64ZPD+7gaFlAIYWyCD6ha2nGalRd46gUAmoFJvkWOlVk4nxNk1pPCjGlWFUW8ogMaIGENPGc628Ph2SJhVeikhnmui7G+1gB1vYwRbFxjaTjW3KrSHlzphiu6SeVFSj2udXtdQqqSVJV1ONa7LSSxZrLc44MikRKkEqjZAKoRKUTtFCeWMff0/GhXhQbS57/6mWjCtDJ1H0Uk1hfZpNriRZ2kPa2hvuptwlfeU029fWASCCVPv8qFhDE/KtiSvcLvBqwGJ96nstXFChLs2g+siJh19wTfxLCQ4NvBb4cefcx4UQPw38JPAP2m9yzv174N+Dd+VGYFwyAkCs86Aw+EWNgGjUArxWtNtdGQ1frcLGCDlS08TB8EEhfERWJUGNyoML0jGpLRPjGJeGQVkzqi2T2nhVykwNXCkg1RKQzWmsQiGSCrUMovLfLUyFLcb+32SCKSts4f/VhfEbvvKWva12gUMKbGWx2lAXBp36z5mywk4miHyMKMbeFqkLRJ2RJB1KE1zGYaYt/t5L60EeAaKlQNeCiZbktWVcGfqpppP6Go/aSXKlSbIeovKp+R4grfT3mBYfhkpyvzZ+pghFsYBESB803L2mxoGwIKVD2uC9k6KRiLE0OpYWX60X66UEx0ngpHPu4+H3/xMPjucc7Uzctr1hYVqc1EqJNm2jN7z/Ej9+MH4TFTxTddHUYOx2jbaNbqtSCuNdjOPaS4utomZQRInhc6Iq4zcVeHdsoiQBG77AJ0TkY5q5hHCiWpwxMTEKCBHvRCGzhKT2rwkpkUmNyhQ2qJFSCWQiUalGZ5Kko5FZ4j8rxTT3qvUdwppQkeelaHNPESSWJjof5zXVklJLJtpSakVhHH3rcJmmtgbrpDfakw4yZCNjyiCNoyHhfI0GNYiCRGc0VU4tgHgbw8eB2sNYh1CCOrjCjQBhHUjRlP7GmvhYB381AHnJwOGcOyuEOCGEuM059zjwbcBXruazu8kBLMEJQqjmc9NKNNcyJIFm0aO7tnGVKkEigmeqrqb1Cy3XaAwszapRXmKMK8ugNOFfzagyjCtDWfssX+tcU4+QeK0s2Dz+PmJmsSImUQYJoBRCa0TWQXVKkmBwS63ReUo6V2PKClcbTGVmg4aJQmiFShMPkk5G0stJ5rrIrINIUn9tpRpPknc1hCznZo5C5WA4ik3bC2j8M+aJag4lF7yBc5nGORtUJEGm0+b5nGil8zuLsMHjGNKlEp1fChAbPHrMOjWcczjnM3Br4ZDOexCPPeslRqxw9PGxS0k0rjReam/VjwMPBk/VU8BfutoP7ibPcG4qNYybSo1YdRbLRRMlvcS4LDAms4U9lwGG0+klwJjU7rLAmFT+hLURoEFHz7QklZI0RHyzAFYdVCEIUU4pfTZx3kMBVml01kH3xuR1iSlKDwzjcHV9SX6VlCJsfuEBkoWIfcu1S97z3yFlmFQ3lRzCkSnJRElSHdzg2j+PdTa4VL2r1zoT/q52rZQmZjMJIchU6iVjHcBwOYAYAUw8QOSlACG4eeMrBocI0kM6h7WCYydnS3/jnmkUgavYYy8pOJxznwOuGL6/3LgcpUxbahiCTtqSGuBTLbQUlwJDBmCY0gNjt8iPqpRQjSpVxqKk4I0aVIZhZRjVNaUNp1pro8bs1zxRZFrSTRTdVNHVkl74W6J8SWvcC04IUAkkHa+rZzmqO4c0NdQVmBod08XDvUY3bjNX8agXPp1cSOmDljH+EQKWTgVvW5jbWFueKIF1kp5Vl5y2Uggm1TSyD9PAYWm9reU1UYGSGmVskEaSVKVIZxHO4aQHxQxARB1SYkoSlRKj/BEgIgKkVb/iC6N8APPhkw/xox943xWN76uVHi+15Phjj6g6NUQIwaMSHz0alREYUUWI8YxpLKMMdecxi9TtMsC1L0qy06KkqZvWhJQUGn1YyahCiZAP5D1TuZbes5MoOqkvV43u40S26qWlwunMB8pcjgv1CjNDtDa/EFdwVLiWbt/aTPFnSLvwHjh/6ksBifRBOaeAVPlcrtI2cY6JsiRKNDZI+5lr4yiFQ0tLVRsm0pNZSOuQxhMpJDoLalwAtwv3ijfQ2yqWDgAJNwz44KRQcmaNHfDoyYebmvg3Hb638Xhd5kx93nFNg6NxeOABEpPL4hZoS5kIjETKBhh6NzAaER+BIZvkRadTDKIhPqiMo6p9Gkpt2i5Of10pZJAEPqCYBnB0Ei8tOolCh/wtH3AUrTypkDinQn15O0fKTRPpYrATRyMxp2WuoklSlIqrY0SJkgN/MKfIpvZCSUWuPLiHWjKuLJNaNiUA1k3tqmhbWQeFcSTWoWtfPKVwVMKrfEqnzXeLAIzLAUQIiZbaR9FVvEMvteOzOuf46Ilj/M3fex//x3c9wBsP3+NtkRgQvFoXVWtcc+CIpasNMAIgYhBw9yTocJrJmLjXlhhNkG8XMGCqToUKwljj7ZMFbbMx65Zo183CTeMAMZrclhoxqzTei5LtzQrga8otPg3GmGmiYln72E0MLE6Di+6ycYh2NmsM2MUUmUTGfyqwldBQ8iRCoFTwrklf21FLR6KgkyhvU9Vq6qre9f26ZXrUxlLLkOsmLNJKpBFI5eMrOOclo6WVnmN9HhbeSYKGRE6DhBYxdYNLwUdPPMzf/L338bPf+QB3HbzHq3suPFOr3DnumasZ1xw42iMy7LlgiPuTk0Zn0C01ZboRwsk+E+SrdwHj8upU7VoJeq3EPPDuYWklqQQtZRNBzpQHRDsCnwS1TgsQkYsp2AvRvokSKRIuFAZ2ippBWbNd1gwKw9a4CkQLNcPSNIFPCMVReso60s81C52EfqaYTzX9VDOXaTJFcBD44KenNTIIZ4PXyku1TClqLciMl565FkFqaMaVCbX3PqkyOgYiBatr5s1XMSrrKXiUFSQq8baGixkIYrqQ1gTbQzRBwkQp/7KcZt1+4rQHxs98py+Eit+JC/Q8Ulxyav6pduX+cUabszYG/iyuAQvQ1Dh84tTDwPQUVRIf5DPVbCyjDYwY5JMeGAYxTRoM8ZP26ZMpgYm2TYhZ5FqQq1nVydsWBOqewgOiyfcIer9OcUphnZdS49oyKi2bk4rNSc3FccXazoS1nZKNYclkUlMWNXXpWUjaapXSEp0q0kyT55qlXsrqXMrqXM5yJ2FSG5Y6KWARWqKtnx8RubZcix9KKKSUJDoL1DvTqspci6aqclJ7aVq35iee2p7/SzSuYEVQr1TSxHEEzK7JTAxEoLRCK9Hk0AH8xIfu52cDL9bMvsDbNyGj5BufmqeN+BjfiAZ4o+CEWYi8UhDVg3BaR2A402LPCx8KhG/ezsiwLXXKBD3fBR3fR9q9MpTjLxEZSrLdmbXONAl5op1rFG9Yem+YNxTSkDbu3aSD0rA5qbkwLDmzOebs5oTtQcFkVFGMSspxTTUZYKpiptBIJRlJ3iftaLJuyqRF1mAWO0CQciohsX6zJfjNSGOLmeY+BaJJsMxVQpbkVFr5BEvjSAzkerYsoFkS4edMR3XHeYeGCOoVOvMlsSHW0vBjucBK4gxYzyyipcZKQaig4d8GitEZWtfGgxnYfGbU1qsb1xw44mgCf2EW2oe/BD7eYiL8vl9/p88XkkGNaU6mWRsjVg82dobUTa5WLBZquy5VMHJjVZ4OKe6ZlGS6lW7e0PYUHhh11RAUiFAt51RYapnggnFdO+8JGlY+hrIxLFgflOwMS8YD/68Y7lANd6gmA2w1wdaBlEFrZJJT50Pqcg5TzzUBwkQJr24lik5i6NcKo6fuTWGtT5+pJ01RV5Ptq3SgFvJVfTLpkKQdEqXIjPCp7xISK0NFo50hPzDWhQRBH82ug3qlpUYovx7ev0QLIC64ea23EYWv3Yj2x1uO3ktlPSWqbYmHtl0K4gUD5JoDxy5n5iW6owA+FoDx7971APcevQ+YVswJOyUlE61YRhsYTqc4lc6yIYaoezQzVKhLjVSWMdKdBl0/kw5RDpHVGKoJsvL5US6wkzSxCeWj37ITgnFR9w7LaHAh+c8yqSyTykfC6/izGGPKEbaaYIqxP2EBZ7xFbALBg067mNpiKsOoNKHAyYaAqWuix/77TeOksONhQxwB+Eo+HWpEsg62LlD1BJF0SNIeSgpU7eNAlYDaKmqxi1I12Ii1cGDik4oQ02gFCKHZ4cJZnDMIK8AalFLYsNOjJ84J5xnb495wLgAi2hyiAc/VgOSaA0ccUWpYR2NvCAEfOxmA8c4HuOfwfY3vXQl89udlOV+l9/GHQJ9TKVXQ+QszNSYNU+5c0SpjjdIiltQmrkZOhr7GuhziJkNM2GSuLsGEE1F51kPw0W+hEn+Pu7wrMbcp5mVJLdFaohKFzjohOj4bCJQqQegElXbRWQeVKJQKmbpq6maO126+zrnGSWHLwt/z5e57PMRlHUR3zoPb1DhrybKuz98yPoYhhHcRu1DF541zvDst5oHF7xa7ACJE4xyYWXhrQNSowD6ipfCIkFPXdntYN81EaXmsn3dck+CIwGjPgRCCj544xo996H7+7Xc9wN1H7g3Gtx8STyvja4zDRhJyVmqoZAoMMyWWbqoHW3GENjCSWIMRgVEOEcUIUQ1xo4FPOZ8McWUs/rHBt+ynX+jE/z3ohsLZJtdKCw+6XCv6ecJ811BUBhsSGaWcR6ddknIOW1fYcMJLpZE68a9lmqyjyXspnU7CfDehm+mGWFoLGUoACDZYNKzqQDVUXnLvTvnkTBneI4JuK7EkaS88m/S+aLx9oZVscVMByqtXM5tVTQGCqUKMQjLVzcIaCuETGfElxU76W/O9Olp7pf1z16HzfOOaBMfMCE//0ZO+DcC/e6cHRvROxTgHu8mcIUSE5ZQmdBcwSjPrup0JsMG0JiRWE2JCOatnKHGjgedvmgxxk8BpFcnQnAzcTfFeWv/vrI87CO/67WlFkevGdZwqwUam2R5XVEVNVRpM3cW1WBB9LZbnyU1SRZJp5jsJS72EpV7GSi9lPtf0QoS+cXu3U1Da9xTJ26wF4+2S6ASRMT0F7wKXQpFkPaz0pAyOkDHNNGDnnKM2BLGx66gPAImvCNty8cKMF4uwBtGD78CrVgEIIu6R/3+IkF8ufvPoyWP81Q96G+Puw/c2KoMKrltg6pVquSa9xFAzNC5tYMR6by85WsE+BISIuxKtaHtVBnYSTwfqqUELr444i3O22XAi5jjp1GfHKt2QSkOrmEgJ+pn2vH9C0E0lK72UYVkzLLwUKWrTsKy3YwyRZT3TiixR9DJfkNRNJb1E08/8v3RXXlecl5h/JeoKkvAMBNvDWe/xqytcVSAKTyKNSrwhr7SvDZe+wY2WrkmFMm2Xko1O1ucAiDD+u0RbvbKB6MLbkza4bKOabZ8jZcRdJViuOXC0DxCIrbTex8+98wHeHIChg8tWtr0TMz0d5FUDI0afp2zrXqVqfPRhEwsXFtDUgf7SThMBlfJEy1FS6MRny6YdZJZD3oO04124KoGg5mjhpQSAEpp+oqhM0lBnxopH56YlrLsDcDJsEl/EBYlWMzXzTRWkiLGhwJiuUn9PoQOTlco/Rx0SH/2XBGodGs7cSP0pTI3Unq1EWefJpK3DSUEdfA7GOZywweskvWQOO1L4hw4AKYMEaZFbuKkkl0zT/V2IxEewScQlQPiGtjnieOSE78H38wEYhJyhuGF9A5apvxwIBrignYZeuTav1SwwCmMbMBocGVP9XCGaOgdhgi3TDn7ppFFThJryWgmdIJK08fj4qsIcl+Q4FdoS4Dd4ilevMuWC/TqbEh5P+yutd7wbexmJG7NvlWhFs0MxF0lLhUwzKMZQ5LhI3NYKmookm/J2QVB7vBorpfap8zaWsIa5dFN3dcMdpmRTJ9KM5wDINKHSoIUC6Ym0XYwAv0h1Ko5rFhyPnnx42pU0pCULaEjPlPQ5QmKXnbEbGIbnB4anMm6NAMB4KHm9djaTV6aZr19T2m8u8K8FVYoQK7Cx3DYmGqoE581bv3mVQBMSCIGG1sYa71WqQ9lpK3W9GbH3h0qa4KaP33jCO8c0ygwhaCYUMsmbLAFhch+bSTqI3BeCudrzd81kFUQiu3gsR6+X1CENRaCEow6HSh1gawDlWoRtnniqmVcREieVSlo2SIimN3EZA8qzPzZVHg1ImiWbMcb/1PNWvdjxSChk+cXvfn/TtTVmoTZZsUDDGBJGBAah1ZjBR6Bjb4zolYrAiPxWsaRUCd+iq90EU8pWqnhMPZH+FBWZX2iPopjImDT5WrEOPYK01bHA378IvQ1jukldhJ8TKMeet2o8xJXjWW8SNN4wkWZefev0kHkX0o6XUqmXWDLJfQuEEHsIcg4pUmSaTlvI1UVT084lBWH+GV189pbtFDelB4avz6+FLw2OKSZ1nOMWo6GwPvWjEsGwlsK7p5kFCGGdBSBVipbgnN8DpuVdbHfOvVZ4q17wePTEbIP3eFh7vbOV9u1M0z+uGQEYTipvwLWSCY0NUfDgodpt+EdcRTZyX7jT6g0iJJHYTegU5/RUksRTuwkw+nytyoSoe21nTvCoFibKd3wVdYEsR7PcVdsXMQNP0VMNJ9TjAlPWMxHydmlsutBH9eeR88sNZ5XL+h4MaRcC23tt3SX3IqVCqx5JGvLSQo29u2Kaf6gVD7aTinMV2EG0FNSOprtTHC44P0So+aiw/hohkCe8KPUBQSGmNqSz4AQEphNfKOhhZHcZGHH//KnmrXqx4xJ6lfDsTb2CaKlTl9nhLmzi6IUyrZwp6zzxWyyzBRoaHyV8PCB6keL3NTU4AXiCFCen6kY0+mM3qco6isJhnA2Rd3z6S7hUrDvJdMxC9ZKDusCNd7Bb65iN80wuXGS8tkWxOWCy6bmr6onBhfiH0BKde86qfDEnW+zTWR2Ql74lmwTvWdJ5o14VTcu3cOrGxwsSbFoglpEk+bT/oalm5zs+d1OMFUAWpLp1Di1kMMa9se6C0S5CnEc71eRgKRs6EQhBIhRO+vqPSA0tnPNOAOEltRKNdyG8z4/IrXwt8Fa9qPHLl3mwdt/xGXWqrYPHgF9QpyLxm1dl3LRz7KxNPcNvpVWQTC2AtN2fTfNIaE7PaOyXgUm8DCyIkyY5zzWqmxaiqbkAGwzxoA7YGleMscNtio1tRuc3GV3YYrQ2Yrw+YbJTMjaWKtx8IgQdJcnnUsphSbcIuVxak6c5sttHdGt8PrMI9pZlYmBQ1E0Kup86f2+XS79PpUJrTRKcH42qJWJN+tTwj8BQMrjDm7pwDwygSXmrQ9s1Hx8J0tqFBEKp/Jt25xJZTyQupY4Fgz5b2rkGGC+EnueaA0cbGG09ksZt66ZR3vYIG9cFdSpWrvncJVokYsFuDh/TSjRJhW1y56mUijcjcaq5Ay8lgqHvKUG5hM+qrFtcVhJyLelq35xmqZOQSEetBUpM3aWuLqknBfWkoBxUFNslk52SzcowDk4F8FH7wjoWd0pkItF5Qjrnea8IqR7+cPX2Rml8zcjmuGK79Nm7pZ0GFXWo98i1r333/FSKXAlS63PKtFJopWj6l4uYNTWNXDcBO+eCV8PvYuFco5lBTA0SoWDJhT7nl6pXzfQHSRJzsKRQ2ODe/fDxh/nBFjCudrzk4BBCKOBTwCnn3Hdf5WfCT/+7bG/UXUZ4XKCoTllCqekuqdF+uwr5B5HGJ6aJxGh4EjxivmNr88kmYly3ah2K2jOUbBW1z64tDKOqZmdSU9S2yYnSygfp5nKLJQkg1GRGkOoUJ5OGGFpp3zFKqum3P9+QSvjPSC9ihU5wMsHplCpItJ3CF1Jtho61w8JQh3wqrRSJEszlmm6iGdWW+VrTT33pb618i2bbHB6KGLMWBMK6XX5VYaPiJv2mbuWBEj7d8ALg+aik83BSQb3ya9u6rrMh+8DviQ8fn9LzRGBE7qrnGy85OIC/AXwVmL+aN18CDIJxDFwSZW2J9qbP9y6pEWHkwrWVYybbVopI7hwj4WJXvXf8Tg+OKQGDB8awNuxMarYLw3ZRsz2p2BpVTQ/xGFzME0lRaUzw0qRS0EkUuXJ08jR4nPqI7hzJ3DbpXIdqOCEf5T4VfbMgu4xa1VnMyBdy0rmUdK5DMtf1yYKdPjbtYFRKMYn0QjXbk5rN0aX3GIOG41LTzxNKkwTnhQUSnJNIfBDPn+4xYdI7ptXM31ou8FCQpN00e7e9zuAPHBOkh1d/w7WCCotUjUo1HY6Hjz/M+37zvTzwnge5O7LxO64N9hEhxGHgXcA/Af7WC/18dHc+xxdMJQciSIspv1WTohMu4zN4p52SGjVKiKla1UST3dQTJgSx9YFzgS8ruIXHZSB7qzwwNoYlO6GH+KSaetKK2qs3SnoKn1Hl67RzLZjUgm7axeVzqIUVXFXSDZ9VWpH2NfliRj/w5QINT242l5IvdMj3LtLds4Re3uOvkc/h0m7D7zuoDKPKMqqM73Ve+LbO8R6VECTaEypEj6uUYT5Kg1aSyvr6cBNjMjCTsiOl8ipRyHny3j5HhW0SEV3oBRKzqS1eWriwZnWIgZjgVvfzH06qVnr7h48/wnt/4wd44HuDxHCXmijPN15qyfG/A38HmLvSG3YTSV/2PZf8wes7riU5LF5nNewqqw1i2rbsB58aEul8Yr239xw1fv/YyTR8n7c3/InUdGY1hsLahmN2VIZcqNAyuW4xIVYitFLWkknlSQuGtaFTKybKobOcrLOAwKGlQiQpyVyPfGXqzjVlha0DbWhgOoxu3GxpHrmwglraC/OruM4CpcqZFF5qRKKESTVt61wFjt94j8Y5pICx8s07y2A7ZVpSGEMi1S4CaMcM1ZGtQWoSqZFaIAInLyawnDgPPLGLIt05H1GPLl0DDZs6BOeHk40N8uETj/De33ofD36vJ3TbHXS/2vFStiD4buC8c+7TQohvvdL7dhNJx2zL57gwLuROxQ5P0FKn7LRoqX2SxHhF1FXVjArlK/xkOzrdEstO6WCAzqZ2eIfZbJFUHEoIbGiy4s0A0VCWxv59RSBnzpTX2WXWR0uFVAm6O4db2oveu0MnZP26upwJAgqdIvIOMu95VaobYhv5PHXSYVR6jt9xZShq693YrSpHGTN1iXQ+okkzsW5qq7m2ly96c+MENMVlwdq2BmTtI95K+eIlvGpcWW981yFscele8I8ncFhJw6buQsMa5wQPPXuM9/7W/Tz4vb4V3uWkxbXAPnI38B4hxDvxJdjzQoj3O+eeP3S5a0y1ftFIjbaBDFN1yrhpcRSEkyvGr+IGEMzYFzP+/FB73gwR3DBSh2sIiFT4curd0qFCsJNqagdSGjIrfY2zgCzxrY/zRAYGdn/PhfFuXyE8wHKVk811UN0lRL9AmAJl6lAkNSV+a2pVpM+WdSrDJpm3MWoXJMbUpRwTFtPAWGKdJ5z2rIc0AM4SRSfVZNozSMqQX9YI6TAHAlpSwzQ7WwjZ6LRSJaRSh4CfHyHnt6nVb9bYgcNhBOCEDyCGe/ZCRHCsJTHuO3rfDDAsu653FfvqpSSS/nvA3wMIkuN/ulpgzNQEu1hTEG2HqWkeXbQQYhrOzZx4cbSBEWvNLwFGaH3WnITxXqRCIJvobCN5hCc9nmhHrqcu29hPvKhMw6Ergz6fKN8XvJMo0pDaXjvHsLZNS4WJBF35mgktewjZQ2atSH17nqBhn3dAXTlsaZoalYYtJNxHKn2MRQpBlngWx6q2M/cZQdzPNN3E9zBPtGpY61WYyyg5hLW75sx4CtDIdKjxzS53e7LcNDkxDhv+bmlVE+K1gkdOHON9v/neGYnR4GcGZFevY73UNscLHk3UlnAYtQACASRhQuLGgKhS0fjY4/tj6okQUb25MjAu6S0R7sXrvA6Cf10GVUxbR09LXKoQAlLlyd1qN9Xl/T2LVjxlStYQ1azaWMZWMN6lJLRZxneVcTVjmgcWvEQx2BbmJV4jUTLUf0i6qWQhT57zPvNAiN1LFD3tibCVbKliDZFFAEZLtRLtAG1NAxDbAkgd3LwN93Gz5p7FkHDYATz07EO+q/B7HuTNR+5t6jriholSo03pdDXjTwU4nHMfBj581e/3Hwq/iZhGA0wnxYXJO3bcZ1/6ArZLc6bawJhm9E6ZSnxqhJ0Co5392jjkveHpYvRX+Ao4GxgQRTDqG1IDpptz2l9cND0KwW/q+D7jpq3HyqBmlcYGJndvL1SB+XBGGkWaIC3JAwVpGpgPpyWygkx6nq34nbS+NwJv9/1qOeX/bfdSjC2gsYHis11kFjlxW8FBkJcwiigZ13EKkDhsXOQmf2qaUvSmw57p0M6AKf58YcCAPyXgeDGj8Ye4Szd8VCc+ctxn78Isl2wjZWAmm1cK0fSmkDDDVNL4fXenhUPzN+FswzOr3TTt3Pf905eqc0xVung/ECUeTer8MGz8SR0oekae0G1rXLE9qigrQ10a6rqVUiFBB1K3PPOMh8u91JfKdlP6qUJLhU79yR9bMzQpOEwv1Tw6Ub8PX7HLeREzB2SYiysvXrC4g7TdzSjiTMwbFLjQb2O3/SAcmFAc8vPveoA3HrqnAfHl3DVu1+flZd6ze1xz4NjtYbrca87BR44/xA/9ji+E+nO//l2XACMOIXzkNrjfm+o+YgrEbkC0A01xZ+8KPqmQthtjJ23wNmocNCrINIg5tZNMYD4pwlFe1Z4bdlwZNoYl57cLtnYKxsOSclxRjGtsXWJDCzGpEqROyTqatJMw6qUUgXk5TxT9VJEoST9RdJLQMlmJGaLpMAvNaRxtF9M6jRvCaqLkjZ9qzZeQfjcjme1Lzq459nNnpQhVHV4VFiL03WjPcuMuhjcdCu5aG4ijn8OZ+ULGNQeO9rjEAxF++ciJY/xwAMZdh++ZeS2ORmoABMmhmG7cSwjfMMzMepNoqGl6kMeXCDxZcurpEbRS6aPXqw6u4bg5hCQRwvfLSDLyLGVU++8sjCItPVJqYxkWNcWoYrxTMhlsUw42qYuxr9IDhE7QWYe6v4g180ghGGeaopqSEvQCMPqpoqsFypSI0nvApgFO74aKmcWemTEJxVJiJobQBjkEZ4VzOBW8eNZMfbS7d3CYAyGUl76AaxI7ffpIGyA+OBjsJhzK+fiHZ5mJXzH9jhcDmGsSHJcDRPzTR4770tmfe+evctfhey5rY0BLnWpJDSFaqxv98sE/6Rc6+tVls2kaYDQZucHwJeYAOe+tCYAQxhMviEDCMFNVJwToBJV1sEkHkfXpdxYAhbE0XVsjBakxlroy1OMh1WRAPdyekRzOGaRKqLIeJtgjOmTW9lNFL/U/+xrkeBNRDBryucvdk6dIzX0Vo8pwSiNjleEMLMJ8hXURNpQmS32pu7lVGEUI9E3dwS4Y9169gkslSFwqEwjdcCIcduzKoXrhQLkmwRHHDKG084UsERhvPnzltOQIjCg14kYO2lB8E7Fwx0dj5fR6Ii52lBwBJExBGh3Knhu39NyzVeEpe4oxdrTjK/mKsWcqaXFZyU4f2e0jF1YQtqbfW8GkkiJP2C4M/TyhkyhGWqG0pE2hMyV1CH+QsiGU7mWahW7KfKZZzBP6qaSvQQ3XEeNN3NY69WiAHQ+mVYWBJUVmHUQe8rLyHugKksxLvKaXyJQiR4hAyCC9o6Jxgzs3K8XjXLaMLyl2eSFF0MrCgsndJ15rWBzSiRnvZbRNXwhnFVzj4ICrB8ZuEesBEaXGZboiCenpJSWzWZ9CTtNSQpavYxqY9u9pZQmHIJioy8BlFXqKj3Zwox3q0QgzLqdctFqT9HJUr48sJug9Dickc91lSqNY7iTsncvYHpcMJ5VnWO8teopRQJaF/5lmpJ0Fst4iWSch7yaszqWs9NLAWaWYSyVquIbYWcNcPIfdWqPe2aYel831hNaoTKO7HhjKhGBjh5ZqqZq1MC03us99U0HF9FSnzjlmaJLiIRSksZudxib/CoT3xMUT7Qp7QTAFCIIZtfaFjmseHDAFxs+/03f0AaYifZeKGydJMk05b+996+LvAiEVboZaYRp19wbq1EhtY8N7cL1bVoRm9JHW0lWFr/ke7VBu71Btj6knE0woRpKJohpkJP0JWSCA863GEuazOSrjWweMqy6T0Hfcc9IlJOM5z7QOqCQj7fTpzqX0FnIOLHc5tNRlfz9lJdfMpQo92UKMNzEXz2EunqVY36QajKjHBTYmHGYanefY2pACVmtUkiKyzlQChDSdSLbtWzRM5z3SGMkAFNHMJLvc4tOeGxJ/KKmpX5IIkBDmmK7KrrVthrv0jy9EeFyT4BBiOvmX0POEYS/Rgqfp0lEnbTxGzEqWafxo9m+RgMDEzN4QWLRMmcElAiPDNYRvziJa/fZ8wVKNqytsUVGXJdWwCEVIFpTEFBWm8sDIlUYkKVJqcqVZzHOMywM3k+e1OpVqsk5BMckwsd+5lmS5ptPPOLSUc2Slx9HFDgfmchZzRW7GyNEGduMCdmuNYn2TycY21c545l6cTb1qVmhv7BszVd2iOhma+xQxG9nO9knxB5FPXtQiAiVK7WmVR1TJLpvB4KLKuwsZzB54f5LjmgNHqH4EAjCCV+rNuyq8dk9Uu6Q1iuu2W7UZu3zq7Ui7iT+djyw36e8zHhtf82yl9KqFDrxOpsBJv9F9/+9k2u0VwFiM77jp71FKqmSEyjYhyTxAVEavv4LtJCByEi2YyzQrcznrOxNfQBXctVkimcv9a/vmMvb0U/b3M5ZyRU9UyMFF3PY6ZmudaitIjJDZawpv1CvawT9fIEXg3PLMKakvlnK+6rCqfXu22s7u3zgnUgrPPGJdU2Yc12DWzTX938bLF1ziAndJUqJ8DnEgL/PS1cQ44BoERxyPnPTu2l9416XAgEtFrG7NUjvoFoESh4VmcWJsZDco6sBUEuvOYw+Kdq9z46x3P+KzY0k8E7nszeOKCa4Yk8yVHhDxJI4nNl7CmKrGjEv0aAe700FlHaQQzPWWUXlCJjMWc81qN2Gw1GFUm6abrVaCrvbeqKVuwkKqmEsVXVEhhxcR4y3MziZutIMZl42kAl8jgpIh5T0j6YUiqbyLzHvI3jw26eCSTpPIWIQaeV8e7HPB4pzENtfS+nZnWkaK0FA+y1SCt9dBNJLCNQCyQlzigdxdEHmJvcnsYQjfwLxVDT3Pd7+fu4/cO+P9iJMQR5yM9gTOqFsx56j1xwiKaGBG9anpCegCEZyxFNY1qRb+ewRaWnItsU7isFgkvbTXXFwuhBiCVHSkb+WlssmMri8T32YMwJYlYjxAbG/4LrVAN58j6/bopoqlXDeNNGMDT61k0xjT16YLVDlETnYQo03s9gZ2PMCWpf8+KVHZVJrJRHlan25OutBD9hdQC6vIhRVsNofN+pikwyiUAUeAxOaZMfVECIFWjixmOWtP++l8lA8X4kFXCuA19h9+TVRYwDYAtBS7AoTxp7vsnohkC883rjlwPNKiV4kSY7aXxXTzz/x916xfSRJfDTBiW6/KOAprG77aeF2txLS7KgrnLM5JumnP0/tIidQJIsuxWQfZ2SQdD6nHJbasvDTBn+AyTQLhWY2dDEFKpLNIUyLLEfNJh36a43LdpJ3ANA1E2BpZDRGTMVRjxGTgvWWToef1lQKZJqRz3Uu+V3dSTwbXX0TOLSL6i7P1IJULae8udJe1TQ7YdJ4d2jlcyMUCCDQkrfwob1BI5xpu38ut1bS34OwB5/uMtFz74cXdnFWSWXqebzjeqsgicfcVVKnd4jOO5+IiuFwWkI++hzZn+JPQV7nRgCQCwyf8TbNEtRFUMgDHOupEhc9Lct0h66fIpItIuqj+AnK0ghvtoGIPj6qctiqQoVWBkJ7RvBhjrUUUY0/BmeWBiiakfc+kZkRiu9pfsxhji4lnfq8rEBKZdUjSrImzCCE9s3qatYqk+rikh8362KxL4RSTplDKA2NYG6p62pMcpnaecxK0d+4q4fsCWmgqC5v6DDFNC7ncGs4s9OXWVoiZrIk2ZxUwQ89zuf2ze1xz4LgSvcoMKAQzxjfMxMlmvSHxAJv902XH1FPlGkPVBYO8dlMam9o6tHTUVlAbF6SMokqhqL3KlaVzZPkcohojur6nh64nPmpejHFVGRrH+Ei1s7GdmW9y48pJE2cAbzDP5niBbxkQAoOtVHtnTeDsTRAhQi104ulDg5uWJGtoQ63OcGmPwkJRWQpjmBjHuDQMg8Ro90KPQ0qH3rXFjfMeLRFY3xvPoPPshLO1lMwuYrzu7t9nU9ua+EZbHdvNW3U145oDx1suo0q1QTHDJdUaQcX1/x/FbtuFfhXDZ9z6moba4Zn4AhB9VHZaSDVtfOPBFBtfRtK2pLKhh2BGmnVIuyBtjawm02i68fy0tiygnOBK3+/DmdqDpw4cVM7OptI3E+Oj50LpYBknwVuWeYLrLPeesCwHqZucLqdSbJJjpaaygWZo4nuAVJamxn1SG0rrCetiM9FmrsRsao4Cn+4uQnLj1U357PxfIZ7RvtZulcwCDze8VQ/yliPTdszPN645cOwelwNG0Ewvfe9l/3qZazbXDtFZJ3yGtfB5PVpIMmlBxwoI6f34oXtqU6PuIkiMr+ATkqESbE5q3yJNK3ItyJRqjOdEdknTHllXeLCELlGiGiPKCW48wA63QyuAEjuZYIqqsVWaSLuUje2gsgSZ5w3vlez0EJ0+LutC0sHqHJt2sFJT1M43uywdlalnKgar2lCY0MBz17PG0RSMtQq24rPGviAxTUeFzISYpfCC1v2S/w/GdwgkKuFX5pFnPW/VL7/bky18Q1cCwqyH6VJgOC6XYn5FYFxhrqKtKFxY7NCnVwSjUUuFNpZCEFQoSyEc2omZjePtE69kRwI3iAbztA4ijUVJ2tdX+Eo7QVf3yfM5ZDlEFgOE9oqKMzUUY+/ynRTUkxJTlDNFSTZLSfCeJxHsC9mbR8wt4oLHyaY9xrVjXFqKug6sJ14qFIF9pAw2Vb1bMhGlg7giKGJRVKYkOtSMKDmt1Zci0vRcamM0KSiXiXQz86dWtF2E9mt45839vzXlrXoBuACuUXDsTiK7krid+UzrH8zWFl9a49Hyrcfgk/QSRDuBkV5dUsJX2kUw5LW3L2rtqGpJaSwETqYy6OSTyrc5NnZafgq+TDVRgm6q6CaabiJZzBMWOwndRNDTXTq9DCUVAoGyhroqkcW4cb8662Zcwc38aOVjFN0+Ym4J11nAdJcYG8lgbBiU1rMcFjWD0jCpp+2Y2/fpqws9kBMlm7ZssbR3prqw1YyzKYLaBYrIvt4Oxu6WIG2A2LDWlz/k7PSnkBw7/jA/8Bvv5f3f+yBvOXx5FpLnG9ccOC45RHYD4woVaDOpCbtAcbkTJSYjxqIbhG8iY/FVfol0jYfKKkFtBVZ79++kMhTal7bqWjCpDRbhy1mNY1TUDZtgFVzCEMgXtKSb+c6xq/2UxTxhtZuy0k2YzxRzvRWvv+NQoQWZrg2mNigzfXaVJt4d28uR3TlkfxGxsILtLmG7y2yXlp3SsD6qWBuVXBxXXByWDCYVo8JLjUiuJoUHbzdTZFrRzXRDrJ1qQVdrcj2rJqpGdfJxDNXKZWsH/C4HiN1r0vQOd1M7Ue7eBEI2a//Q8WO89zd+gAe/90HecvTe2aRQrqgsXDKuOXBcMnajJU5Si+kwvq1NvLA7UASXBgQbMb/bPRI8ITGtpB0Tqa0jVYrKQlVLhrVFFQKoqY2XHNY5JpVlMKkZFTWmttgWo7nSkjzTrPVSVucyBvP+NDdzOdZJFgJA5ILvTqvDpqi1oi596ocOwNBz86jFVdTyXmxnEdtdZqu0bBWWszsTzg5Kzm5POL81YWtcMQn3E9UzqXy6eyeJVD1ewqVKNhH4TqrpBbUwUqe22zQ8l4s9jucK4jW/x2BeWMfopQrOXxByBhj3HL06NvUrjZeS1O0I8KvAPvzz/Xvn3E+/2OtNMRJ9/WJWjbKznX4uL5qn6lrbJRyN/BbMpp/RUxDGhjixhVqpvCTIgodLhqzSorZIWfvYh7E+7bw02Ni0XgkmqWI8rhhMaorKeGIGB8znCCTz3SWUNcEL5OtAVD4iiRHvNEXkXdT8MnJxD7aziOmtsB2AcWp7wpmdCcfXR5zdnLAzLCnHNXVVTwOJSqADc4rRsuGt6oYiqcVce2Jprci05/dtgBGDkI090KosDOs0o+q2Di6/FO6SNXKhkN2HRkRznzaszcPHH26AcW8AxizZwguDykspOWrgbzvnPiOEmAM+LYT4PefcV57vg34yPRxaAdbWZE4nvh17iNv68mpU1G1dUxHYEC3gmpTzyOIurGW3taJCVWCiEpzWlNbHNRLp67Z1AJ51UFTG8+WGVHVrnN+YoRq3CoAxIYZgrGvp6TlSKvpBgijl6UHtaIA0sUw2RLfnl7H5PKa7xKCGrdJLjHODguPrI05tjBnsFExGvqe5qSNAQYftIaS3heYyT9IQVb3FTkInpKfkyrNCEsnvKsMM+V1godzdek6EIrFpbGIKjN0SfsYR46blsNbCw4G36v0tYDQHY/s6V9pUlxkvJanbGeBM+P8dIcRXgUPA84Lj0otNK8biiK7UOCm1mz2N4kJEjUkGoCka3E2lRWxOGdkObYuLyRpmYCkUSN+QM9cZWdol0z6uoUSKVr5jUySbrmqLaf55pJvaYq1XxcBvzvVAppaqYAyLFJkpur0Vv8lUgurO+fgHhG61XZ8D1VlkZBXbE8PasGRtVHF2a8z57YLhsGQyqignFab2wU2pPJ2QSiRppunlCUu9lH0LOavdlL29lIVc008lXS1JhEFUk6ZvIKZmdhuKBgzxn3Pa17eoMGfNvpjK5qiyNuvVOAZiYqJfvA8/+xA/GHir7j4yNb6jGh1Tgl7o+FNhcwghrgdeA3z8Mq9dlkh6t/RojLUwogr1UMi+bNdezAwXo4beRdv6ddaW8TPcahhZT1Mzal8d18QYlEZojVMpFAM6aY8s63t/v6RRs9RuWwYvMRrOBeewxlGVhu1xRSdV9PPSn9Tau0VFquh0l3wzyaQTNia+KWeSY7O+90qVhq2iZmNccXFUcnFYMSxqqqDOORvsAiXQqSTJNHk3Ya6Xsn8x5/Byl/1zGXu7KYu5akgZZDFAlEOoY118ORNr8cHH0A9R+jiLn9pQ/bcrUSoyxDRFZI26NV03n5YV/Oz4lKKYa/dcXsi2JLmaIORLDg4hRB/4deBvOue2d7++m0g6PnAT8Q4AMbOfwQHHWrxVUa1qnyJC+ML9pjBfRtPOpzJcOoF2CpKgPtjSEyb4VI8AEvCpGDrxddepD+L1sj5Jp0Mi/emfBobBPJGcSSQXtWQyktRFjYn2R7gJazzz+WBSMcgTNic1uVZI6Zc6zxeQSYeGNUQqrEqZ1J5OdFg5NifeVTuYVJ6ONDgBpASd+tNbKYEOwFieyziwmHNw0VcQ7p/LmUsk/UyS1mPkzjaiHOEmQygnfi7alX3a8/TGKLy3FSRCWi6lSaApOW6kR6uQbPfB36wbU96q2jmUY6asebeN+UJcui91f44ED4wHnXP/5Wo+E/OgZkDSYpmIIvnhZz1v1c+981f5vl9/p/fXx/e44JFynjAskj/jPDCM8IlwNji9pBDhA/LS/ARnfcZsK6FvJlU6zRtiAtUZknUWSToLJFqTBcbAXEv6ecLZXLO2UzIYld7eiCWwWiED40gVgnLjyrBT1GiZABaDJJEp2nd59nUVIZ18XPmuTUVgSqwaw1+SpAop/bMq6Q3wTidh33zGnvmcA/M5+/sZq92E+TwwlYwuIifbPlo/2MKVE/8vlgMHUgYREiPRyUwSYOyyFXPDYjaxDWsUEz5jOs7l+MZiThzAXYfumeGtUpexLNqf/1Nf7CS8wviLwFedc//yxV7nEtHp4OHjD/HDARhvPORzsS7H2i0EQSXzk2pjRmgjxr2V7+0I57vJE/vXBXtDNEe7B0ZI68Ban/OkNGKYIoZbyM4ccn6EKMfMdebJej0y7Xmj5jLNfJ6w2CvYHBZsjeumh4cUnoU9S3zrsViK6mvJJVIowFIJ0RR1WRf7Efqs2cJ6YBjrfMQ6UfQyRyEF1iVoJcgTRS/XrPYz9s5l7Oml7OulLOSK+UyRVkPk1jZitBHqQXZw46G3c6LEUBp06g8rFbZXIFBwgfG96c8YGEsi+32UEJGkwf/uGoO6vX5CTKlLrQuxKOfLcblM2vuLGS91C4L7gS8KIT4X/vb/dM594GovcImoDdmXP/w79/PvAjCmZMuX8VTEP4i2NKEBif/Fu6x0pOCZfiTAx+GcRdQ+5kDlgWHLElvXOBMyUNMEl+1gxzuouR3Uwgp5vkDSW6ajE7qpZDHXLHcTNicZm6OKwaRiUtmmeUyeyIb+X8rQHtk6EuMlp5YOE4oZrHVNb8La+lwoKWnaICwD3VTNXLufJ8znCcvdhJVOwmKuWcgUXWVRo7Upfc/OBm64gy18vXl8Rqk1Mh4WQXJElcrpDHTI9NWJB0Zo1umrKqd1+dHGuJwN3UiflqlinG+rZkRcL69y7Q4uvlDAvJTeqo/w3BkfL+RawJTp8OdawHghLjwvF/wJFLe+xXkHlfT5VCrp4FSCkDqke6sml0cCNqhZUOKMw5YVzlrq4QSZTdDjEW64gxwNfKelaky/s0Cnu0BXSxYyzVaRsNmpGVY1o9JSW9tQzGgZiKClj1DH5zfOu3BE6zBox3W0EqRG0k28mjiX65lrdlNJL9EBEN4TNZdK1GQHsbMBOxcxW+vYwSZmOKCeFNhQay6kRCQKqbV3RsSGOT3PceWSrs/21eGf1DNtrmMZcjTAo51xNevVPCseIDYAREqa0/OFJjXG8ZIb5H9Sow2MNx2+10+2u1S6xBGT3S47b8HzZYWbug2d7zzkOWE1OtUInSHVxKsKKkEqDYFYwZMTDKbZsrWBSUk1nKDzCcl4hBpuI+e3UEt7EN0RC515ev0e/SBFxpVtcp3qlqdNCe/tyqQvhW3ddrNjGqEYVK1cKxQhDSQNNgcikFyrpitsN5H0U4kuWyrU1jpmcw0z2KYaTqgnhX8eQGiFTn29uep0Eb05ZG8B2V/A5X1cqDW3Se5BYaGup/Q9MW+r7WVq1kj4lZLONSkku58PplK/aU8Qrvdi+ariuCbB0S5Ocs7NsJC8MdLQX+ZzcaIiKCIlj9g1iba1AlMuWNdcQ4YNp4UizfqotIMsRqBSZGAKsSppJtdZS10bTFFCAfW4oB5O0MMJ6WgHO/Jqll5cRebz6HyeXs+Xoc5lKrRtdk2/DAjp3m3yAjEFfLxdLxUEKmQQ11LQj3MgY7KgINM+UbCbCHQVvFDFDnbjAmb7InawSbHppUU9nrIzqsS3fda9HN3rI+eXkf0Fn/Wb9nFpD5t1MUL5Gveg4tnLRL/b8y+DxJ6+EAujPEjcLiCJ+Lfw0wp3RZqeF1JHck2Coz0ePfmwJ41+1wO86dC9zaRKvMHW5EmFn5cDhaSFjjDpbU9JNOajJyx2GpQSkjq4Y9M5kqyLLDpeoiQZKI1W0yl2xvqmlkXZcFbVk4J0XJJMhg1I1NwyMp9DZ316nXxaY2Gld0lfxji9JG8pSLzQqhsdU/fFNBkwkT7lI9MCVU+QwwFisoPbuYjZ2cRuX6Tc3KKMRG9RjVKBYjRPSea66PlFD4yFFegtYnOfDl85xaR2lMZQ2WnzoBhnEK37aZoHhbXYvbktgYDB7QJJaw6ea7wYzeqaBYcEjp30cYxIzxNFczxJ2hPSTo+Op39b7Mbe1E7Qiqx6YLTZRiKjH3jVKdGCXCkSBR0t6aYLpEkHqTNUlvtItU4Qch3wNR3CWGxt/L/Ck7vZsiKZeMoeNRkh5paQ3XlE1kelXfI0b3qc14EmaHdwbPdo6HKjTSSnqeK+rzq+iGo0RhQDGG1jdzaCtNii3BpSjaasKM7aS7rUqsUV1MIKcmkPLl/AdhYoRcqosozrmsr4Yqmqnp03HZIYo92k4sKJaU34lFDBhbw0//dYZxMXr/3+5wLBC60+vGbB8ZFIz/Pu93P34WmFl2/F6/Nw2vXIMW2a1kl1SUmtiG18vVFuBb5TqqNpRVwZSxm8P9HT47sleSO3pxW9VDPX34PWOUKl6CT1RUqJRkhJuRNO4gCQelxgrSd1y6w36GVVIqsC2S9xVYHIukidkegMg/Q2iHUYpjxOV8owjqd0TAhUOA+KokCUY0Q1xA22sDub2MEm9c421c7I2xfhPsHXhehORjrXJVsOrZuX98PcMrazRJ3PMSgtw6pmUBkGhWFceYdCHXLDtAoJikqSO0dPhoi59ImZ0xT32XWJEsfaAJSWDdZ+1qgJTNXMWcBEV8s3LG/V5eh5QkKCN4ZdbGM8HUpMJ14yPUFnU0Sm6hhMm9GbSMljooHsK+WqFkAyLemOfLxipZMwzhULaZ/OQgelUnTWweiUTGnv2dnWDUeusw5XG8y4oAr6X1wY6Ryi43O6hC5xukIkGUol2ECONs0hE5dwNcXsYi2821nUBaKuEPXEU/UUI9xwCzsazACjnpSeFhQPCpkodO45rNLFBQ+Mlf24/gqmt8LYKrZGNdsTw+akYrv0nrZxSNGPhVJN0DP13FrGOrQKDXDktPWcL4jyc9AuNbBhfQRTu6KdhRPVst3AaEuNb1jeqt0sEvFEiUHu6F2STZMU/6OpRhPTqrQpx1U0/kTQh/1fjQMpfWMUoIkbjCrD5qhiXNZNMxgZMlcXuilbk5SVXkLZy5hLJYvz+1E69QTMSYbQKSrdpNrRfhMGtkGhpI8SVwZXTnwrAOW7u0qlsE1vC58dLFWClMoHMIm5ZdMNE7EviDlhVWiJUPhcqGLko9zjIXY88N9ZmabJqNAqeKNSdMfbF2p+EbW0F7m0F9tbwXQW2Sx84dS5YcH6sGJjXLI1KplUltrYpg6kk2oWu34NIreVitJMtPu+x80cnQ8+JcQBRgik8wCJThctpypX8+y76kcifr6heat206t4MRqGFFjrwmTSvA60CIynp2jMtm0PKbWny282nI9I6+YU8wVL47Jma+TrLaogYhIl6WQFy72UrfmcYWHY10+pbcJivkymUq9mZTki76C6W9SDgZceLcp/ocQ08h6YRmxZIIQMDel95m3TG0MqlFCX1GTFevrY7FMEcESQuLpsqH9okiZ9wFJKgc69Oqg7KarbRc4toRZWYHEfprvERPfYGtWsj2vODUrODQrOb0+4OCwZF6aZl1gDApAnkm4o4dVBxU3ktOFmk/Zu66nFLQSEuJIQoUwB4dVfCHXoUzLvK/Egf+TEsSZJ8Wroea45cLQfLBrRcQJmar7D3xqxKr1PX0LTJTY2U5nWHUiEqHFKk+gMlMA5ibEm9Ns2TXpGZSxFbRkVNXVlsOEo3EkUm8OKrVHFzmLNKPI69VIW8x69+RSpUnTew26tIzubuMnIb1RjEEqFpEVPrBYTGKfDb3isCZmtxuvREoRob4cAjMBXJSJ1T6hH8Z4LiZASF/iqALTS6E7t7yVS+XR6PvVlYQXXW8L0VhhZxeao5tyw5MxOwemtCWc3x6wPSsqixkSJqiVVbVHSHzIQjHHtVaxE+hbUmfSlx6IuwqG1K4NOGp/urhKUUCAhtmb2TCNiZs3bMyGE4OHjx56TEPBy45oDx27eqrZHI0qRpuaY6QQ1hUutvtjTbkO2OaV8ezP/epLkoJQHiLP0E8VYG7qh2WT83qr03VyD5U45rqnKmlHpJYxP9rO+dUCmmZ/fj0xyROYZD91oxxO5makUE0p7FSzNIM2RaTZtqxYZEC87WvrFlaq6hAKpkWmGddarZko3nFjte5CdHuQ96M5jOwvYfIGt0rJdGM7sTDi9U3Di4ogzmxO2BwXFqKaupz3H0zx0nyIGIIPNkYR686ZQyvmaEFPOrokQPpO33alDgRSqWWfBlJB697pPgfHeGVX8asY1B444djOQRCkCs3pmU/YaPVMxczSwAM40kAdf0OS7wSCc8wDROqQ2aCrjM13nOwk7k5ptJZtUhar0nYtqZXzQr7beoxQCX7WFei7DWOjni6RJjky7iN4isp48Zy2Elf5n00lJKJyUzeZB7FYi8O+1IITFydYGExJnfCKgkBpyg9hdkyIlJKnvARjqQkqZsz0xbE2Mrz0fTMtstwfTakJrLEIIkqBKSSVDLYqmn/qWa/OZZ1iJxVKyGHsyu2kxS3gGiRC+u5WwtqkBES2DfYYtpjVmgTEldLvacU2Co+XibtQmf8j4SbrcyXBF93fT6jeqG/gcJVODqpC2Jk27ENQOS0JtLaW1jMuacZAaVen9KM6CsZ6gQEjBtgydlloGQe0SKqvophndXo6qJ4i6AlsFNSg4KcWuzR9O/XapqQeKD0u2A8feEA/dqYQI9ooEab19of1zu2jkO0e7FsNKBTLBJRlGpYxqx2hSs1Uazg1Kzg8KTm2MZ4BRjqtpHXwiEEqiE818J2G5l7DST1ntJix1fT/CbiJJbRncyZNpBWFDkBG9K2GdxIyD94prGg/FCIxfec+DXmJcYW9caVyT4LjcaFIIrjCu+JKYJqPMbpIKjGyM1zTtomIbgV4WkuV8fUUV2EOcdeHk9PT7prJUpWE4qVjb8awdUvjUiLqTUFkotCDTGVmaX+KluYqnbgCxOyjYRJqFbzeGUiHlHp9KP/P8l17X4nPJKusoJp7xcGtSc3FSsTYsOb89YW2nYDipqEqDqayX5tJLCp0oslwz10vZO59xcLHLvn7Gnl7GQurzt1Q5RJYjqEuErWYMcH84hJqPmcNBNCfic81SGxj3vAhCN/gGAMc06ewyr8U3QNPrT0rlT2Znp2qGs77IT1hvb+AgpKBH9UKG+uiFzoLfbCIL120F3qRAKUlVRvcuwevqGJWGwaRmI6maqHBlHP1UkWlHIoNbs9nU4ZowE7BsOJ9adnesd4hp3wBCuGkvvub9IrxfNe+PgbU4X7FW2xJq3K0niRiUhu2yZnNSsRG8dKPImGJDNWGim+KsLJTYHlrucN1KjwPzGfv7GYuZYi6hae0sgjoZJtCrkUJPATGjRsbuvbLluqaRCFHIPNy4+6PEeMHbCriGwRE3vrc1wt9akxRHPBcbP7gQvne2kGAkgtrrs6YKKkyNqI03TMsJNja9T1Jkf4KoJsx3F9F5hiLzqRDKuyLPJJKNpPTSw8YSVIkM9JilcRRVzbBQIcrr2xTk2nPlahWi+ARASNEYm1Jeng8qzoVxvhR4/eIGCFhZXMJKGiK69vsiv5YJNR+x0MjYaRtkQ+TD9dkB49IwKA3DwlBUNaVxPrCqJTqVSK2b500yzVI/5UCoPT/Yz5qWa10K5PYmohz4qHwkhNAJpJ7P10X7SoXWCiI4DFTi7a/mOabPFZ/xWMic+OV3v597jk69Ui9UpYJrGBxxuAYgl6feiU5aE0ooEeCkaGIZSAWm8osRWiJ7tWPs+1mEnhlCacRgC9lfQJqSXncZ3e37E1P6+opOqrmQT9gae7K2mDYd/fx54hvXxM05qX2dRlFbVON1m967CIDJpKSTypDD5WZAEqWmsZavfu0JLm5sYh3sWV7i9ltvBjs7P3Xg1Kps3PT2sg14mvlzruHLjRm1Uvq6d5trpBQUWmIdTTXhQkc3JbYH5nP2dTVLuSarBojRRdi6gBlseQ+dcz61ptNHZl1fFJXkHghBWjSVg6G1dW2nktLf4zQ7+4d/536fUrSr49eLGdc0OBrX3i5gtIvq4zo3TS4FCBvjHgqpFELqkGdrIal95NmU2IvnQxekSZN0JwdbqMkItVKQ9fewp7sY6iV8EdJCJ2FjVDEqpsFBFYJcWaLJE9lU8kVy5hD/mxJPW09MDZDqwCxYK+YyRz/VRG1by5B1KwTj8Zid7c3GZb29tcF4PKbf7TSbqAGGgUFZN9y47V6CTTp+iFzHYR1NJSG5Dm7ZuuHThUgZqlnqJix3Evb3M5a7mqVckYw3UYMLmPWzmM017GgHWxuElIEBPoU0xeVz2KTrD6uwii6oUdN8stl1tq2yhV941wPcHbhxX2ii4e5xzYKjcWK0fo8T1ujOrRGbqtSEmIeL3YQFUviTr7ISaxOyLGN8/gznvvh59maaDEU1Lv1Jnu+QjXyJqN5bkdqald4qSvhTs58WLOaJ740XmNbjJtvNSB7TVCyO2tAQJ4xKr7pUxpFpxUI3wZI0RUvt5p/gT/pECTpaznhB08A/FQkLgjnRSK3tsmY9BCwrY1ESskTTDfSfqZJo5e8zVaDxErKbgM0dlnTmPrSIxVKK1Zg6k0n0cA2xfZ7q/EnM+lmKjR3qSYlzkHRSJpubXDhxmv3zB8mWFiiMRVrfRloKn2TYbuG8e20/crzdh/5eL90QscK52R/wwgBzzYIDZm2LS4ARJvDRkz77MpbMupbukAiBcJ57qnawXVoeO7nG+sU1juaWhXyewc4FpEiZbA5wxqDShGo4oVNWUFcoa9HOsdTfE1IhMpY6nvzAl2+G+7OuVc8eTj877VA7wUyTGyd+w45KQ6IElcnpZaq5lo8AT6n7FeDqiq6eLr1xYOsSJfJGhEanRLyHSW1Z2/EpH5VxITfMEzD0MoVWvkowJm2KkC3rHQTBNgpAVeFe8kAm3U8Vc4lADS7A1jnqs89SXjjL+Pwm5c4IU1Y+G2Cxz46ZMF7Yx2dP7XD8yU+zZ3WVWw+uspD5SkehNBZF1UJ+O6nwRz7wA/xc7EMfHBQiljlf0Yf//OOaBgdMT8ndwLA4Hj15jL/ygfub9/mWWzSbdKccc/LJr9FT3jB9ZqvgD59Y49kLQ+6+dZV33vgKJl97mH5lqQZjqnHte2kPJ9igC6U6QSuNlIr57hKJVJSJw9rgkxf+fgyuIT2IxnOs7KuMI5UCiWGsDcZan36yPWE8meAOL3Pdapdcq0AMF5LzpM8pklKwsb4OtkY66+lphGJrY535+QWcdD7mEebMhk0PcG5rzInTG+R5jpnPmO94AodIEp1rz3ii1Ww7AR29aw3a/A8pIZWCjgY1XEMM1qnXTlNeOMvw9BqTtW3KYYm1jqSjSfs5RZpQH3kFx57a5NjjF7h+9SRvv3UP1y9kaAkjKzl8063oJAOCI0C6xnkRgWFjpq4LuXWxPJBZO+pqx0vNW/UO4KfxB88vOOf+6dV+dnep7JWA8XPvfIDv+/V3Al6n91m1NaPacvbESTp1jZpsoKuCA/0DJEpy5swOHxiU3L7a42aZwclnENuWelwhpPT1DUqishTduYDNe8g0B5nQyftkQWEStvLBPSlwOsUI3xK5jAVLdppyXhpNJzVYHBujhNqOOXdmnS989ksUd9/BO+48wGpH00skiRQ+Ac/5TV+WJVvbOzihG73BONja2uFAXaECy6BWkkQ6n6ohNMuTlMefeJpPf+xxXvnql5N3D5Cn3mZY7abMZTqoNoSmMzE50LceUM74XCjncEmCkwkOkDjkZIAoBtitdezmBSbr20w2Bky2xpSD2jfdKRJG5hyDm67jmR3LBz5zmuHWhNsOzHOgn5Bvn8IlGZVe4qtPn+LAoUNkWjKXJZF/D8BLjDAiQKIzJHo04555IeOK4BBCfAD4a865Z17gNa9qCE+Q+m+AbwdOAp8UQvzW1RBJt8eVVKm/8oH7+fl3Tus9op7vasew9OkPXzp5ntftyRCbZyge+ywLt76Kt950B596Yo2djRGfO7vDrXsP8ZX/8zfZo/YyNz+P1BKhQA0Lyu0R5c4QuThEmRDhNhVSSEQ5Qo43Ybjpn7c7j8r66KzfVPXVLeMSIBtVnL54htGFHdbObHL63Bn237DEK1cFN84J9vcUmNK7M4XyUsgS3MPB5dzKGKAuKSpDV2m0xFf+OUtH1MynKVTwqj2Sk9ctcvrcCXq9ikGyiFXz7Fm+jn5HN9eM1XtagowltcUAN9r2X9hbxHYWcWk3xI38XNjJkHJnSLk9ohoWVOOauqixtWX97EXW7Hmuu+tuPn92h52NEXNLXd560woLZ79I8bXPk936aurVRb588hxmbpX9/ZRuMgWtX1vRHIoQAOJE0+ymDZAXMp5LcvwS8N+EEL8C/G/OueoFX/25xxuAJ5xzTwEIIf4T8D28GCLp1vjIyYcaYLzl6L2NKpEqiRSOSsOktvz+J77I+fNr3LpwkD3DHc5+/MskX36am//iHr7jVQf5nY8f57HT24xvvYG5o/s4+fGTvPxVi8hg9JrK14O7ypO5ATjp+XGdsyhTMn7mqzz2e7/LvkMH2f+q16L3Hva9v9MeMslIdIL3LRtkOebMU19kpRbcMSfID+e8bv9RblnucYBNJh/9L6hbbvUNaDqL0FlEoHGEts+hNVl7KCkaik0lBNKUiMk2MvBPTb7+dd6xfy+v2n8bX784JNeKG+Ydy9Umo6e3OHjHy3FJHtI2HMKUiEmBKIfIyTb1uROc+fxnuHDmLLd/+zvIb3kNteiHHDAvrTzRna94dCZUaCa+L+CpUydZvesI46Xr+PLnnybrJHzHqw5wM2uc/r9+g2ow4siRm9kpLZ958jynBo4/d8+rPSmEmvY19/UcDmyLmOFPYFwRHM65/48Q4oPAPwA+JYR4gJYN/MdhKQzjEHCi9ftJ4K7db7oSkXTr9cbI3i0xBD5wBtBLBM55l+pXNi6wtrbO2qDk+OaYm1cPAXDhS2dY/viHuO++v8iXT21xYafg8+dGvPEd30M9/s+UWcny8nJDYgb4RD2psEkHk8+zNfFT1BUpX//qlzn55SdYf/oUe6474mlrVBKOd+vjKwiEKRmeeYqdLzyMlIr9+65jz/IecCDOfo7NRx/m6cdOsvGa23nNn/lu1I2vgLSPkwrjYHNr21ctxih6ML6NdWxubZNnezzxmamR5Yj62cf5zK//Fs986QmWbjnIwTffw4H9t4BwqMEJzDMn2DQV44WM7r7rPSE2gR+4miCqMXa4jdk4z1ce/iTj0Qh95Cg33/YmBgWAd2bIyXZIfvQJjTKRZAsZQgrWLlxg8ZV7WX7H9/CxcyMu7BRcf3iBe69fZPLQr3D+86dZumkRuXqIZzc9I7yUa1RbaywdvIGsJTm0gKrx619+j7yY8Xw2RwkMgQyY4/KMN/+3jt1E0ld636MnvDuv8VoQYxnhdJnseDbw8ZA99SZvuXGF33/8PI+dH/Cq/Yc5+La7cL/3cQan1lip1rn7phU++KWzHHtijeVXHOaW/+4vU33lEbYGY3pOo2uwRYUpaoROmJDwucef4dPPnKeyjqM9yZEjr2Tvt6wzOX+eiztD9qkE54yXHrICJFZ4d+vmxYueSrQqQZ1Chvwns70RGmHCqSefof+lL3DLdXdCklHXsLUz4OTJUygFSajRFnh1q7KOZ0+coNftouZ6pGmHesvwtS9+jjPPngRrsXWN3d5A9S/471s/g93ZgCRl8+JFDw7nkLFoytT+GZRmfTAiWZ1j/sAtjA/ewQc/9RjPDAypFLz+hn28el+HRCeYovZ2mgSTCIaipr71AHte9uf5ml3k2FfPkmnJG29cYaXeYP3UGovXL3LwbXex1jvMV79+hvmu5s03LrNUrpOvW5K8h8s80ZCWvvbfGDdL6/PHHM9lc7wD+JfAbwGvdc6N/kS+cTpOAUdavx8Of7vqEWs3Hp3xc98z9VpAY7SJyTb29BM88fu/S10X3HXP93FhtMDHnrzI7z6xzrtf/70cXVilPnccsXWOV+57GecGS3zxxBb/5fNneM3RRV796vewt1zn4uOfYPz1pyi3RvS2zrPU6TCql/nkiW2OPbHGxrDkxn197r5+mZvv+rP0Ruc5WRVkNmFR5wBTArKsR2Eda8ky6pbXIaoCl3aou8sURpCs3MTKTa9mdfMMmJrh/F6+cHoLtXWcnXHJxc0NlHB0tCRXEmm9imeThInxDCBf+PJXWFxcYi5PqIdbuCOv4ND3HfS1Kgv7qLqrTIwjUw7VWUDvHeOSjHW1yJ58wVdWFsNQYAXoDhtmwql0hf53/HnK3l4euzjhkWfO8NS5AUu91MeBhnPkT32dra98heH5i6QLPfKbrkfd9gY201U+e3bAZ549w9a44lVHF3nV/h7i4uPM33CQ5Te+keEtb+GDX73AM2tD3nzzKm86kFN/+Nd4Qne47dvejjx0y8waw6VsLNHd/WICgs8lOf4+8H3OuS+/iOtezfgkcIsQ4gY8KP574Ptf6EUi0+Ev7OKtwoVoaiNSHcXZ43zpdz5GXVfctLjKq296Kx978iJ/9Pkz7ExqvvfON7Nv/w2wvcZquca33bRCP9N8/KmL/OanT/Hhfsobb1rhja/4Lvbeto47+yRCKUbLR1gfV5TWsdRPUVJQVIbPnt7i2c0xK90eh+eXKdcm3CIkq/M9hKlxmWJQO544dYHPnRkxny2Rp95OOHt+zLObE85tT+ilmgMLR9nbS+mi4MIQLgzRUoYe314H96nvBQiB0JZUZlTCMTGOMxfWORkjyuxhkC5xYVRy9omCSX2aPf2M6xc77O0vItNFJsYxODvCrVzkxv3L9KQK1YSGte0xX1svOJcc4PROwfq5DS6OvPG/1E9Z6KSU1rE+rllePkr6SktiDOLgzZxXy3zs5DafePppNgcFK3M5b7p5hbsOzbO3vghVSfrKe7jQPcxvfOEcn3jsPMuLHV57cB73xT/i6Q98Cq0Sbnj57eSHbvbPE9Z6t8CIteQvdjyXzfHCKkNe4HDO1UKIvw78Lt4Z8h9eKBAbep7vfj9vOnxP0+LMEeMKEMnrbXeJemEPvUNzDM5sUZ4+waFXKl51dJHfWxvyqccvsNBJeMfNh1g0Jfb4l9i3sMo7b3oF+/sZ//WLZzl+covfODfgs4fnefNNq9x64FvoJp5orSgsRxdyblzqkEgorePZzQlfOrPNJ5+5yA17+tx3wzJ6fIqJLjh49HpM0uWpcxv89qe+yrMXBqzOZRxd6NBNFeujisfObPPUyS0mo4pOL+Xw/j63H5jn4LzvsOQr6Xw1nRL4PCSd+QRK6WvKUzVNax8XlrVRycmtMY+d3uHUuZ3m2jcfXqCf+e0wqg3HN8dsjipOD77Ae77lDu5YzWFnjdMnTnDG5JyuuvzRU+scXx9yYLHDHfvmuOf6ZVIpPM+XdeyUllKvog6tMqosj18Y8sgTz3LitPdw3XBkgXfeuY9X7+2gT38Zs7mO2neErbkj/NGTF/nU1y5greNV1y1yuK8oT59ApYrO3j714l5cdxnwuWmVnSYWtuHwYqUGvMRxjsCoftWs6u3RZpF48xHPjRsNshjwcw6K0OPuTJ2xsfQy9v3Fv8qe41/BVSV68xT3XneAyli+cmqbM5tjjm8XzM/twz39FXa+9gjZU1/mDa+8h/1vuo7ff2KNzx/f5MJ2wSefuciZrQmLXc1cqjm8kHP9QkZ65stUzzyG7C9w+I63IMU8H9wY8+S5Abft6XN0SXHqq1/g3ONfRN30Wp4y81zcKRiVhk4iObTgs1cPzaUshHZjJ9ZHZInk1v1zHF3ocHDep2bkgRRNiRBYdJoaX/2nAC0cqZKkCjra0dGCXirRQjS9P4rKcv2eHq85tMCNSzmpEqyPDOcHJYPJmAs7Y554+lncMxtUT30O4wTitjdyZqfgyfMDAO7cP8eb9ij42jHsYIvk6G2UB+7k+HbJM5tDtouajWHFs+tD1gcF80sdXnvdEm+/eYVDxSnKY4+ws75J57rrsHP7OLFdcnZzzOpyl9sPzHHf9cvorTNw8Ag3fP9NyMN3cGLlThaNV1GHVajHEYEm1Vd6XbnAjW9g3qo2MO6JNcFS+PbATjT09bWFcSj0f/T4Jr/zka8jypLvvO3N3JRPYP1ZDtqKv/DyG/n6wQWe2hixNiy50O+x78ZXoNbOs/Hlp8jPrXPkdW/gfa++ixM3rnBmp/DkziHdo3aQSIkebzD89CM88/tfREjBzd9zltfd817ODUqOrw89ubXUCCGpJ2OoCpJEsKefsn8+4xV7+xww67ivP04f2HPgJl77+kPslAYlBJ1EousJoh6FZDKBsxqXdimMZVBYJiGBMFOCfirpKYEoRyS2pmMNS0pyeG/G6w7uY1ztwTrHfKbQGyewTz0NUjJ3+HaSw4vkIR1FS6iKCfVohOj0cFJjqVjtpxxd6fG6/X3Mww/yxG9+AoDr3r5OZ/EgSvQDc4vgwELOkcWcXCsOzGUcmVOopz7J1qc/wWRti7kbDqCvv5NzLuf8YMhNe/q8/Za93LSckV18Coox8vY38+Q45Xe/eh75zBO8400dAHYKQydRvrGviDls01qW3U6sb3jeql+6DD2PE57MLRph4PtXAHziyYt89KEvsH7mFI+98VX85HfcyuG6ZvixPyBd/BQvf/lbWDqwly9fGPL5s0Netucwh+55N+nyRxmdOMnoK58n21zjhv1HuaG3jM362M4C6+Oa9ZHxGb/dJbLDR+jve5LBmQGDk+dZGpzlFfuW6WhJP1O4JPPxjqrA5vNIA0cXOyznmv1sUX/lEba/9hQAvQNPoVf3sZik3otVlri8g1rcA/Or2Hwegju3NN622Bx7g3ypkzS0oVpIz3M12cZtr2G31lGTMf00RSQprpgwWT/H8OxFABY21zn4ym9F7J9jfVz5fOXOAvrg9d5LluTMZ47b9s1x62qPzuAM68fP4qyjv69Ldvg6bHcJt11xaD5nKVesdDRyvIUstmDnIvXXjzM6fQohJSuvewXq5Xdz3C3y1TMDhBC8ev8ch+rzVI9+hNH2Dt2XvZbTdc5Pf/jrfO3Rz7Dn0FGW93oX/KS25IHuJ0oNKabAuNL++YbkrWoDo52WLoR368WUXWsdeSCc6uXKp4jXBcPtgrVRxeFun2Jjh82vn2RPXbP/zX+WZxPFR55a53MnNnn90UVe99p3s3DbGez5Z7HDLaoTX/dUOsailvew78ZXofv7eHpzwucmFTe+7Du47vqXUx//qk/D1gnLWnPzSpdMSworEEtHQCqGIqWqLIu5ZqWrkWsXsUIxd91BZH8BtbgKgLl4nnrDu1p1fhjmV6kXD1EYLyWl8eQCqfLEctHWUEL4HC6RQZqRdRbQQiK2N6i2N/z1lvegFldRi6volTXsYAukRA7XWFlewDhfLjtI+/T23wbWUBjHQq7JdZfFXOEqzeJrX8PCq16JPnoH692DPH1uCMANizkrk3PUj32eemsdhETmPcg7dG57OXLvdWz1DvDp0zt86rh3Vr75xmX2pzXlZ46x9tnHyZfn6Hb7XtXbGGOqAusEncwDopP6BMUkPLOne53umSg1LnewPte45sBxuQeLAFH4hDOhBNoJlHCkARzvuHM/k/e8jqdPX8eBxQ7dRGI6B5l/xctJn3kKnEUNLnBwfj+JEjx2cotn14Y8ub7E6w4tceTofpZyhd4+hzv7JNWJJyjPnkbmPRbuOMj2pObYE2tUxvHa65Z4zQ1vZU9XkUhJai3LHY0gGKqiw7jynLLWORYy5Q3qzgLq5XdjuqucGlYMC8tCrth3vSPfPAVYzPxBTpeas+cnSClY7SYsZJ4oLVGWXPs4Rx4iyJVxbBTehrA4DvYPsO+OPeSHTgOSeukwp8ewNTH09yn29zRqeN7nYoWUk63CUBpLV2u6SQrG0UskvcS3MCiSvZjb38b5Uc0nT2/x+eNPkyjBvTevspAp7FN+rlSakF5/C+y7AdPfy4VJzamtkk8/dY7PPbtBXRluP7zAobkcNTyPsZb56/aRX38jdv4A8xPNt73+MKduXOaGQ3v4rpft43/9NCxmespoKWclxosFBlyD4HiuB4s09g0FmhYNA/ddi5Z9N8PFZYmdX+RirThTK/p3vJ352wbInXNgDQf7CffdtEo305y6OOb89oSPGcuXc0031ezpdbntyBvYc+g2kpNfBUBOtpnPNRvDirPHN3nmmQ2+eNMyb7ttL7csd1jMFN1MYpxXAQaV5eK4YlRZ5lPdMJOY/l5ODSr+4PNn+cgXzlCMK/YdXOBdr9zPHauHURJOXCz4wplN1nYKbtrbZzGfp6MlcrJNolKyNPcuzHKEqCpkZ4Fq5HhiY8RT5wbsXch59YF5Di0cxRj40vEhv/OFM6yd2Sbvpdz7igN8280r7O9GrikvfTYnNd1EskzCXCqZSzygK+PYmNR8/eKYP3z8PE8+tUFZ1Ow/ush8rkOUXJLfeBscvoPzcoHH18dcOLXOqKzZmdRsDEv2zGccWOxw19ElDs0lsFGT3nkXur+HHdVnUFqWcsF7X7aI3KlYWVFct+LXdqWjWgQTfrTLE14MMOAaBMdzjchlpIL7TpjSU+sD9Sf+K1/9V/+R00+d5va/8AY6b//LfPBr5/n62QGvu36Re47eyNLkPOn6k7x6fpWbX7WfjYlhp/DEyMc3x3zm2Q02tgv2LuV8x+37eMNtb0GvPQmjDW5bOcI7X7GfP9SSnVHVpIQnSpC6EjEaIVRKlvQYhCVMpaCXSXraJyqapMvGuOZLJ7ZYP7lOXY7IOgnr44rt0mAtnNqecPLiCOs8OcNiplDb5xD1xOv5Osc4SEyFHG0gTMFCtkIvUYxKw8mLI1b7Kf2gklwclWytj9g4dYYk7/GV5S6vO7zA/l6OKIb0dNc30AmMjhLIlO/8JGxNknYbgrtuqplf6dDPE952x15uW+kgt0/AygHq1Zv41Jkh/+2rxzm3OWaxn3HnoXleeXC+4bFayiW9cgu5fhqXdLnYO8xDz2zyhZNPc+v+Of7M7Xsofu+Xeew/f4Kjtx/l0I//dwDo8SYq7eJUOq0vxwPkxQIDvsHAIZkyG2JrRF0iKs8btfm1Z/nMly7w+KmL7P/6SdK3Wo598SynHnuGE6ePsq+f84b5FPPMF6H8Cv3+AvPdOUSnh11Y5OV7VlnME37nC2d45vgWH7Iwn2te1t+DPPckc5MBbz94Pa89cBNbhacNnU8l84lDjAeeBwvQaYeOFizmXr7Np5K0HqHGm4hkzJH5Rd7+sr3Md30p6htvWOZV+/ssJo7CKaCPED7o94q9fRaqi4iN09BfoM7mOTusEAj29xZIR+uIjTMsriS8av9c47W5ZaXL0fkM7SqWb1pmqZPw0aM+ce1NN65weC71tRhVQdoVLKQ5IniAuolEU/uDx1bIwrLYWeDOPV2OLuRYB/OZZIkJ6vxXoSqx+2/hsfUJH/rKWZ49uU1/Mefum1Z485EFFso15OgMbn2IGWxhdi5iO33kza/j8bUxv/Xos5x/+gRnXnYD77xlldFjJ3jo6xe5c5LxmseeBkCU40C+oBCBM9j+MYEB30DgaEdCXfjdB8X8JsyW5jiYGhb3dFl55S08M64pxjXOmmDIh+voFFf7VGuzcYHiwgXqcUnv+sN852u+k8X8KP/tsXNYC+cGBbcsL5A6S/XkFxFPf5nlhRX2LO2FfA5nM1ydgs6waa8hYOsmoKTFOci1RBQ1VCPk8CIr3RHfed1e3nbDEtpV6I3j1F84hivH9A7fwq2HX85Kbx4tBEtuCKefxoyHyJVDnBlWfOrUNgJ4/aEFjmR93PmTCPMUBw/cRn54HudgWVXIZz5JdepJFvMe33njnXzb226gsl7KqZ1TMNqErIuwNXnqJ0dKLzUAXNr15Ai2Ro42WK5LVuoCJjuY4+d9HQegD91ElfY5N9gCfODv7bft5a5Vgfvsb7P97HFUlpDt2YPIcoRKfIUgnrBBSIE1FeNhxdq45uirb+auY0/TzwzZ8jysg00yT5TR4uB65PgLI42+3PiGAEfbXWeDdS6EwukOKvG+8Gf33sQr/v57ETrBXP9azp6ZcP3RRa4/usi33rrKHatdxGAbcfg2zNweajRpsUX+tY+z/sgn2H7mk6xubPCme7+H/d9ylK+vD+mlmkFpWF4+jB4PqddOU587hdm4gFpYRR24Dts9wo5LPcOIFPTwZahaSgrjqKxF5gtoZ1HuAvbiaTj9JLocY7fWuXjyPJOLO6RzHRZ1hl7cx8r8fu+a3byILcbI3hymt8rTJwd8/vgmAKu9lIOHVlGdHq4YI4frLC4cBKlQmxeozp9g6+vPUg0mdL7+JL1De0nmlyDt4PIOYn4Z21ulyuapjPUEEUqAs1RWMDQaYx2ZSplLNXJ0EXPmWczWGq4sEWmKXj0Iq0fYKQ0drXjTjSvcstLjBrXF+A9/k7XPP0G2NMfqm96AuPUNlOk82lWowQVcXXLn6jL/w3038tCBOZQQnB0U3PCW7+ONR27B1RXP7r0Zvg62uzyTrv/Qs8e4/7emFKAvNg3xmgeHj2nMdu+xoRS1MtOg2H89n2KSl5MpgT4zQQvBD951lIP9hHzjKewTX0SsHmStfx3/7avrfOaZDW7c2+fPvfxt7J1b4uJHHmJ4Zo30Kx/l+jvfwvzB+dDFyOGyVfq37SO5cYgaXYRiCDrBzO1nrdY8vTlmWNbs62ccnktJnSdLRnXYKiyTuqaj59izZ4k0O43cOIM1NbK3wNyNHeZuFr4nxr4bqBcOMqwsqdTI7hJyLzidMTI+RT1LpHfhGsvYwNzSAURdYjuLVPhKxN7SEZLbJStLe7Gb6568LkkRKkH25hBLByjmD7I2qhluFXQTxVKuEOUIpKKwCWcHFecGBb1Uc8Nixur8QZSQqL2HIethusuUSY+d0jCqLAfmMm7NOiybbcwXH2F4Zo3+4T0sveU+zu59Ff/XF8/x1PkzvP6GZb79pn2sDJ6l89RH+Y6Vg9zzbTdxalCxNqp45GxJrW+nEA551q/32th4MmolefSEB8YD73mQuyPT4YvgrIJrHBxtYMROQE3fOOcojGNj7HX9B//wCUbbJfOrHe5++X7eccsqB4tTDD/43zj1+Ak6exdZ/s5388zmhA997AQnPvcpvjS/wlPnX8GP3/dqrnvPQczJx0Ao5HCN5fmEtNNlbWT40vkRF0cVmZYcml/lwMIBuolkVFtObBc8szGiqCwdrWAu9ZvMWVAdLo4rnlj3Cc9HF3OOLOxl8bqDKOFTX8bGUtSeUmdSWyYXxljrmM81i3mfueWQNVtZbljq0kv9ku7rpZ6nauEg1sF2adgcVGxP/HzkepXOgb2kh31+Vkf7JMbSwWZR8+y5ISe2Jgjg5pWuB0c1bkitNycVp7cnZIkilQIWMjqLNzCuLKe2S85cLKjthIU84ehCh5WOom/HyOEartdn+fWvQx29g2fUXn7mD57ky49+nnKwwYXXvJ5bV3qsSMPmJz7GeG2LpduOcvNdb6c7f4jfe2KdY188w/bamO58CkdhbVSxp5vw0VMP8Zd++wd44Hse5L7r7m11FRYvCiDXNDiAGWAIYq+GKftle0glyHspN6/22JeUVJ/7OBtffZZyWDJ3NMOlfeoRdHoJvb1HkVKxsTHmw09e5FsOr3Lw1rfSVwY72faenFwyTlNGpeHTwZO1f7nDG29c4ZblrvdUKclcpummfkN3EokcDsAasp73RQ5DIxzw4D6nKy6OK75+YchT5weMSsNCJ+HQcof98xn9VDOqDYNSs5hr5lJJL1Ec7Vuu66iQeCiokWwXhp3KsjWp2S5qRpVlp6g5tz3h1MaYwaSmn2tu3TfHTatdFvOEUWU4sTXhzOaYhW7i27opgSwGIDXd+QXmM81CJyFTklRLagPrpeFr60M++tQ65zcmrC7k3H3zCnOppO8myGqI7a3i7rieoVWcGVR8/KmLbG2NSbpz6E6PvJtQOwdpD51nFFtjNr76LMnCp9j3Lfu4abXLJ3opg41Js65KCB49dYwf/cD7eOB7HuRbr5uWRsOlRH9XO655cMQx25MBUIIOgqVQB/0X7rsRKeCGpS43LGaoi0/Bwgr73/om5NwScu91FPMHOKxrfuzttzC67ybAc0kNipovnNvmSxcEh+dybltdZIlN1M5Z9vT3cue+PhcGJY9ZRy9T9BPFQiaZzxRLmWK5k1AaRy8V6GoE9QThHKIYstLJuGG5SzlvWe6mLOaa2jpObk04sT7i3PkBQgpW+inXL3e5ablLqiST2jek3JzUJDJhIanR609jzvsos953BFZuYFx76WmtY38/I1GCorZ0tOT89oTB9oThjs/sPbCQs7/veae0ECzlmlyH1I9igKgLnKxJzIR9/YR+qsmVYCH3rCjbhaGXKrqpZqGfcsv+Pnfs6bPCELlzEdtZ4KKa52tnx5zxJYPsn8/4S2+9CfnWm33ruESy0kkouweZ/7b30H/Fs9jBFiLLUdunecPBG9n71pt4emOMsY5//DQ8tv4oP/pBD4y3XnfvbACwpU280HHNgiOqVNF9G4pWm4KcRPiS2E+d/ggA79xXIYsd3PYzsA3MLePufCunh5bjW2OKLcshV3DzUsahc59l9NXPYcYlvTvupH7Zt/LhZzZ55Il1nsmHpHqVxeUe7uwTsHaao4dv5x23rnDn/j5drbluIaU3OA1nz6O7ffL5g0zyrr9xAyTdQP1vWMwVd6x2feqHK5HlFi7NWTrs/f8njyzQTxQv3zfHobREbZ8Ao6mXjnB6qLg4riiMw4gEbQwupH/gLLWTjAOF0N5+yv4O6M1T4Aw3HT3InfuO8uVzA8a15dB8zi3LOYtMEPWEIyt9RuSezypRUBhc0gnctYJ+ophPIKt2UOtnceMhy4v7eNW+/YHUznBkIWNvuY57+nFcmuEWDvDU2oRjT6wxqQ1vvmmVb71uAfXlP2D0tceRWUL3ztdiVl/HExsFp7fnSfuv4uihDgd7EjZOkB7/LLcCt80vYLM+//hp+GsffB+/9j0PcN/RuyG2sRMCEVoWxLy7F6paXbPguOxoek14MtWHnv0w7/2dHwZg/PBvMzyzRtLt0L/jdjj8cj5ycsB//vgJzp/cojuX8d13X8ct3ZrzH/pdPvKbX+H8pOZNN3+BV/wtuP26u/nKmW02hhUXxzUu6eGMoT5/ElUV7DtyByurexDOoraPY04/gd3e9F1X0x7ZQo9hZRnJnGzhENLVIDUZkLsaNVjDnnuaev0cIklZOXQjb1w5gj20ipxsI85+ntGXP8P4/Ab9Q6vkr7mHxaWb2C4E20VNLxWsLh1BB9e1mT/AxqRme1KTaukJ0s5/jdFnH2F0dp3O3iWO3vlajhy6BZsvISfbyPXHqM88g6tr5NIe5vZdj+ku46TC5nPYrIcVmklot9BLJHJ7i/r8Cf+sgy3mDhpuX9wPKPTOOczxr2I2zqMPXE+tMjbGY3aKmtV+yu2rPdSX/4Av/Mv/zMee3GB/rnnzn73A6g/ezhfOjfmvjzzLeFiy5+A8f+GuI7zl4EHEya+z85WvUI3G9A6sQgL/6Tt+lnv2vRbqktiywO3q5fFixjcWOFrj2LPH+P7f+WH+07f/DG//7R9AKkFveYFszxLZdbdx1iQ8fmGdnYtjyuE2WWeVceWQ3Xnmj+7j+tXj9LcmdJa6qGrCvn7Ga44uc2FYspCnlE4wt++oZ0LXCdKWyHLbJ9ZJiVreB4t7EP0l6oW9DGvYqX1ttxSWRAZGQSXopzlKh95/ifb0OxvnSaxBJClmsEV99hnMYIJOE5JOB60UqdZkiWU8qdmcgOr26K746ridwrJZ1hghyRJNojU6SUi7OYVS1Nsj7Kkn0HVJOreEq0rM1jrS1gilUGnq4w1Zh6GBopaURlBZz3Kigh67sLCfTIAbbIQuVAJZDcBZpKsQvTl0t4fcc4QxgvlOyiuPLrGvn7G3n6Lqiu5yl5svjFlZylk4sg/ZnWdcjahLS7Gzxc7FhMcvjHjZ3nkOHr0FBhsU59eRITfovv2vx9rQM/BPABRxfEOAo+m9IRROwkPPPsJ7P/BD/Md3/SL37X8d8P9t782jNLuq+9DfPufce7+vqlsTzSS1MBAnL8YDGIMkNLRwiJnBZK33B5MwWIwRvOAhtrEdP2I7Mc92PAQTwAIsIgQ4b62XBLCMTeygngQWYOzgrPWy8mKsbgFCEhq6qr7vu/cM74+997nn3vqqulrYtErUXqu6q77h3DPtffbZw28Dl73staxu7HsE5uc8FumeOb4HB5D2HcRsvcXqOQ0ue9KjcdETzsej3/STeNqhz2Bxz31oHnkB6n/4NMwueCIOPIHrU+xrLA5MK5xffx/M/H6xPNVIrmZHXy7Z5TDzCafaADfzsEXl2YmT0sONwzmNwbn1k2HW74aZMfo4wDCYABjpfeN/Q2rnXKb5wIUIF1yMb6Qp9q21uHfmEZAwcQaNAPOSD2giowKeP3W4cH+N89MTYZ70XQh3f4XNt/UEtLKfo2QB5MpO9RRxei7CygW4b8GxYPfNPWatz8jwjeO7wXkTi3Mai4klVmkUJjQGjk4IC7ZwTc7FvW3CI57QYW0RcN6kwsH9DtODq/juv//3sLj7G2gecR7qJ12KO1cuxmXusVisXIj1BxaYrtb4nsefh8c+8QC+8xFPweT7LwHW7mGb/e9/AHANg4Hn+h3ECO3f5L7a9cwRwaDQSSLVj5w4hld87FW46SU34aqDVyCKDmoe851IVYMZatwz87hr5hFhMF1p4JzFvpUaEYR75hHnH/hOTC45D9PFGpKpEPc9Ah4W05rLFzgy8CCsR4Nm5REw0Ew8hvaMSdHME+5beNy70eIbsw73zzosJEZppbY4Z1JhbSXiUbFGgME5+x6Nyer5MN0M5MUXEgPMyn7QeY8EACQ3QVw5D3OaYDYLONUl3N8FzLuY0c4BNmVXlksFOGex7gnT6TlYedQTUe0/wEVjUhR4fw69gHVItkGsp1gkhwcWHvfMAu6ZdfjGRocH5ozfCzBzfGMl4LyJy+iIlbWoBCK0shXcZJoLWS58hEdE4ypYazF1Fp4s8IjHYfLk/ZiGBVKzDxvTA7jn3jm6CJyzOgHBoG4cIgzumnmcN0945LkHMT33UTxHAOJkv5QsMEj97ZPB/uKDh8zZlcxRWmgFywsxcsjANR/jUleXHzyEDshQ9mtuHxY+Ya3t8NVTC9wza7G+8Ejo0fDu2+Cywau1xbnNBZhO2dTaBmDDR8bYTVw2oA0GMUZs+JiZo4sJCx8x6yLWWo+11uPemcfdp+a4e60d1CxfqR3OmTo8+twJ1s6Z4NFdgwMrbAFaqc9BM2E8K4ROCkVyOEyspljrEu6beXxtrcVd6y2+fmqBe9cXWHRxUBO9qQzOX22ABKnnUSM0K9h37iqom+V4ryQFQpOtsYgJGx3P013rLb6+3uKrD8xx5/1zPDDz2Gh9bv/caYXzVysc2D/B+VMuhrmvZnN14xi2VJkjRhYeWlohJK52laoGzf7HIAGY+4RvnOpwxwNz3L/BG98YrjB+au5x13qLfbUFEpuzG8v3q9YwWPZWVqlBzRMshbZaSruSOZRyHY7UF2B//4s+hEsvugozHwdw9fcvAmZdxD3zDl/faHHPqQVmbchYw12IuHedvb6GCI9aZWloiSezDYlTYrWUQeTUVTLIFZBmLfsR1jqP+zY63H1qgXvWWty/3mIxa9HOuUyYMcB65fDAisP6ImBjETiTz0c8erVGF7jWR2UquKrOzk0fEuZzVnPuWm9x5/oCX3uA/RH3rXfoWp9LmBlDqGrHpclSytWgIghdNJjYCVxDg7bbNmLmI061AXevM3Oc+MYGvnb/HPc+MOcyyh0zB1mDB2qDr09rfG11wcUw9zc4b6XCvoorxU5rByd53YAUwkmSd5MiQjRYxMAQSwk4tfD4+nqLr51a4P6Z51OWuGzcogu4d32B1cayaTtUmFasQq51MVsss1MY2+eQ74TOCnMQ0a8BeBEYNO7/A/CalNJ9D6athL7U1fUvuBGXXngVWoHGDCllRJJTi4D7W497NzrcJzXtFl1R6NJHzNqAO++fwxDBp4jVhcPEGThrOD8dPUJ7fn5RpWmji7h/3uHe9QXuPtXinrUWs7UFFrMOi5lHt5BAR2PhagffOQQ/VIdSAg6sVFitgcYRbJANHIEuRswDcM9Gi7s3Otx1qsXdpxb4xlqLxXqLVgpXAoCtDOo6ZPWqcYyQTkRIKzU6y9I/M0dMaENiMISZx9fXuVrsHffOcO99M8zXW8w3PHwrY7AOVW3RTj3aWV8jcG1e4fzVBudOKqz4yPMnz83zRYRFAKzvT5G55+Sve9ZZqKzNPYKsDQQIYm3OQqc2vB77BS1l1kWuRUgEQ6mvgfJNMsrZOjk+BeBtAs/zfwF4G4CfPtNGNjHGRVdJ3jSXGogSXwUA97eepbTo516Yh4iP7ZQS5lI45t71Bawh+AAsnOEiLqavRVGSlxNlQ1Sp+2cd7ptxAs98o8VsvcNi1qHd2IBvN5BiBBmD0K0AWAWIcKq2uLe2WJGMNo0QjsnCGa65HSOwCAlrXcCpBXu71+YdHpDa320b0C18Zo4YuRFbcaHOB2Yd9k96Zkfj4CNvqhKM4tSiL4p599oil1Geb3gs1teHY6hXECP7b8gQ7tFMPGMkgYu3V2UNLKV+/lJigQR+bhsi5r4XLKp+qmZARPnUmXcRG13gwjyG7z9zH1FZg0AJ1kg+j0RaUwJb0HDmDHJWmCOl9MfFn58B8L+f0ffl/5IxnnHRIfiUihocwCIEdALNw6pPfzVzBEwqm8t96cJ1IWLeRawvvOjpGoZg4JAGVZUChhRiQowR3rP65X1EjBHBR8TQIXkv2LoG0XbwXUAMfHpstAEbC492hatCzX2UZxkNDeK++YA28t2iC3wPSrH4kcnRv2PoP7vwXD+98wFzw5WoSJCmO9mgcx/RhoiNBZ+s3PckfS3G4Bxi6BB8zOMsxzwmLXyj5DFkjI3OY66GBRmEsQaJEqw1mFRcVDR/P0X4wAJg7iMCEhprwVWBeZ185P/1Xvq3VoLgW0g/CuD3t3pzKyBpBXR73wu41BXjVLEaxTo0F4bRDewsoQ4GtU3YP3HwgaF1jKR6ApC6fZYlXcEExjCqoJMkoxLm35uEuagmbWUxrx1WmoDp3KKrLXxrUdURKXDofK9WTVHVFrYy3L4lVM6wSmBo6SkFsL5uwBGolWyamTNwNZuQyfDGdPKaqy0mlUXjeFwKk0qmR23R6kdk+NmGuC+V5WqxtjKoajsYg3EVrGtQ1RausrCOS6WtNBbTmmsfap1ELdWm8+YTQCECiIggmMAqENdONGgqy8VtbJ+qu3/isG/isH/iGIvLmFyyOgCgkGARQdb0dSKlZBppMY9iSs8qbhUR/RcAj1ny1s+llP6zfObnwELkpq3aWQYkrRleJdJh0tTI0fefdvH5/NrbD3zTY9qjhx4lAJ+7dvNrEaJSUQ/AIaA0Zx+3KqX0j7d7n4heDeCFAJ6VzqAmbmaMF30Il190leQLs16OVAYf9nXr9ujhT4x0KKdi8XqUGmgkJvuHPG6VILj/FICrzxS9XQf2jIN9nWkDQpBacTAJKUJ0TcIXT96L73/f+Th8zV3ZorQmqBf3b7RSuTVkk6+hvm74SsPH+GrtsFKzetCIF1rvHgGsws09V4J9YMEWsXtOzfGN9Q4PrC2wmHM1o64NfZ+tgassmolDs1rjgn01Hn1OgwP7Jzin6f0FzhpYsDVpEdmi9kA7NBU/MOvQzjr4NiKIvm+NgasN6mmF81YYVvTA/gYXrNTYV1tMpd6fLcag/pkHFh533j/H3Wu9JWwx93LvUOhNYpWqcZisVNi/UuPA/hrnrzY4f4UBE6aVzQYAvW/oOBae708bbcS6rMfGwm9aDyeq7mptsW9S4dypw0o2FVtc9cED+HPSqlN9pV6bLVU9qxy9/TCu/cRDH7fqd8A1Pz4l3P6ZlNIbd/JFxcZNxWaOAGxitEOGu0t80bT9FayyBj4CzkbUguk0qQxi4kKWatUysun5dTazRr3LjLxMzhAo8YURUNWOPx9iA4CrKz1QdehqC9dydSNAsLWcQdU4rDYOq7VFU7lc/3u7Q0/vHBPZIPMuINZs/7eev2gcM9+0smgqi0llxHRLeYwpF85jItlYzhBWGofV1mPROKTIlibv7aD/VW1RNQ7niDNQGWNfY6WqrMl3NAWYK4nvhykbMrReuhH7spE7SG3lTibpxU7M0E4mqZH7ly0YwyhjiEHlmKDxv/+hjluVUvrOB/vdKy8+NAgHIMj6EoBEucZ4MiyljCTdr1Yquxz4msPeVWN4YhcdX9ABRgtsnIWzfIl1VgvX84JUUnbLlcwXAhprMPGE2vAps3/icM6swwMbLdbbgNkiDJiQC91znfF9kypvrBXn8mVWL50uEigyHnDMTFjntma1XeohnzYO500dzl2psdrIhpVLcmPYiVkB8KQMPtwSTvq40XLfVUBU1mDaWLkoVzh3WrFvQ+qQK3OUc+RDxCJEhETwJHNq9RLuEDS0S8asczStHVYbm0/w1cphVU4lgOPUlKl5P8j3he+PK2O88NsIt2qsY+o6pMSl0CrTS6vVmjd6YwMqT6gN28rnTcBsSWzSpGJLUG91sZhWnHGnZkVn+j5MrEWoGOl8vw+YtRHrXcBstcaGn2B9ETDvQo69AtBL/8piRVU5Z0QdsXC2t88HAJMENIZQWe77RD67b+Ix7yIWXRgxhx1sqhXnZOPy2HINcwDRAROXMHEBk44wcdyn81eqPD+ZsUVArDZslVoRS9W+xmHVGVTOiGccI+efqFgU5LV+La1Y7DoBbuAxEGrXz8/EMePp/DTCRI2jzBglnkBKxYnxwg/him8X3KpS7dANVIYORGEZlXQrlUHjEqOPJ4f1yvOie8e+A/GDiBsCBlxOuDYm6+erInXrfJIQF5EvNkAAEKJBN0loPTuu1luPLiRGZo8i9UVtqKUdlbSVM6hECtpCLVCPf235vtD5iHXvcO4kYNay78MHtv8zyjhxSLzck7T/g/apDx9BAoJjbOF9jUPn1e/B2Lgh9X02YEel9nlSWVSGNzPXSGefxoAxxAvvY4IlK6dGROUJriVMXERb2UFlJkc81/wcwrRiRi+fBQArzmRVUUtwpwQcOXELrv3EK89IlSpp1zIHMGQK1Td7T2hxKQGwrzYIEfCOo2Un1qFrnMQ0sURfxJjDRMj0fo3KkaghIpFlYdgDG7hWnopBIiTH1VQDgC4AfmrRyQbz4qgrPp5rfBvqGc4MHJD9BvZRNpoz2BcjfHT8t8R9qQPNZrXF5FOuEt+AkwssRu1rhSSfAF8ZYQiHsKS/RpirKubCAgymF73gccp82AqJLHwkdDHBmcQb3Bl03mDuLBYhwotDE0BWYythjtpSFkrlMwFg6qhfb3Cxnk8LblUJz3Om0bm7ljnGjGFNgXQYPafLFruw7tYl8tQiOosumhxWHpIRdYc3SJ5m0vrbvLEqR6zWGID8HNR2oLAAAj8PSVyOxL2z1qE2Fsk2SNZlVL6EvtoSdByQZY2B+x+SZDYWcVfGSnsWqbLwyUiYTEJIlg0HhUzQYEN2sHFUAKUAigEIYdB+kgw6SPsc/m227CcXz+xA3vPvkQuBcvUg2YZkB6HwxlWo3ASVISwsofIJneE7Q4B8Ff090soJVxU/A4Hkeb7N/BQzIRFgLG45eSuukbSFKw4eEhzdlE+VndKuZA694o1PDEReKAo+F4lX5tAJhLEwxsEZh4mrkZq6l/CiOmg0r0Z6OlEVagNG+FtwnjW6Rf4/dS1XWvV9uXZyFWAdyDrYukEiI3kHsml0Q5YkKb78U7o1CUQmjwFEsLYCYDjk3FieiHFbWUgEYbwgjFxsYihai7Rf9ktyr3O/RAjw5uyQgge6BcdLLRt7VQNVA7gJqGqQgkdVTeCcQ2sIIRL7qoSxx3POJxIzI3XtQPjp2lK7LpKswi1f+TO84ubX4qYX34irH3eImS4CAXwPPZMQkl3JHICeGvyLAXjBogcFz9Lcd8wgUaTL4hQAlpBEFslYkOEFNK6GMw7JNYAbSnYNsUD0oK4D+QXX4vZzoJ0jzdeRFnOkdo64mPFzJU+CH2wyg1A9yRtGNw+sAxmznEmWDtyArOVxgPKGTnkzm8H3KTMbMxqlhCSnxrK2N1HiGuIIPjN/FgTtnJkjeKCMp7IOcBVMM+Vsw2YCmqwiyallokdyDedjOCeRDbT5ZPIdr6lv5RmynikMTlTqZkjG4vDJW/GyP74OH3nB+3Ho4DOQUoAhiygMR4VWsBPavcyxCXkEIkl0M4h0EyDpuHY/Sxugl9pVA1M3SMZxIfqs+lQsjYuNRjHy4vh2yBjzDU5jna0jtXOERYvQduwPkA1DlQWRgW0qmMpxUZuqHjKMPs8Y/r2gtCSQbzAX4xOj/O42bWz7PWGI/L8yQtci+RZh0SJ2geuLa9vGgCzB1hVsUyN2C9B0NddUN9ZKWIeojMEjGQO7bJ5VbQvMILFd8Aktp1fSdQSAdoZb7v4LvPRPfwIffe57hDHkVIHcqxILxjMIxtidzJFPjU1vZDkPRSKJmu22mLHUk78p68IOVDeASjjjkEzF+dvGZolMSaSnHOmplKTeM0DBooWftfDzBZIPSIEjVI0xHBDnOEDPNFXeQJk56gZkK2gl2KUMUqgSKRbSP6hpdLjwGVxbgJlBhsctqlnCcgZJntXRFDqklu9UqWsR5nOEtkNcdAg+bDlGdRRa6wDPc0SidhEZJDKgQKL2FfMr9xYS5ojtgk/kdtHPtwg4sgJIAeDTX/ksXnr05/DRH3onrr7oGUhY7kUlOrPTY1cyRya1ZwOij/f6NxGrHrfc+Xn+jO+QfIvkPevKAOAqkHOgdg6qWTJRM+U6eakGTMUbbDzRZEDKWE4+Y4dTmUJE9B4pJvjQ5Y2Duh58zpJEkXqb292kZo1UoCSh4/kSHCNSikPVxph+XgrVLtnITBgDb64t1Lmkl/YRY/hZi9h2CJ3PzEHWIJoIA8djBDMdkWHzuqv6e4wYK/T+QiQqX3lidAvExSyrq4PxAnxiFHPy0iM/i48+6zdw9YWXCciCyc/KjFAatHZIu4451EIFALmSj4YK2Ir5JUbABXz65DG89MjP8mf1CFaJq+qCd0A1zMzgRZVTg1x/UU2JJXuhHwNgVQCALRbMAyBrEDrP4eeGIXtgKW8c4yyfUFXD+nnFql2+jyjJpTqN7jOp1RNDxpMi3ycAhtUhg2QAglzYrWWI//I5esEvnyUMkYyVMgMRxlnELsA6ixQjTIiIDnlstmLGcJMGblrDTldAkxWY1XNAkxXQZBWoJwzmIKeydL5Xg2NgwVUyRjvnO46OMZ90fRsffeav4eqDVwCuBmwtVskKCcT564XJjc4A3G3XMccmUvs8xDdgaxAZHDl5DC/7kx/DR5/1W/jHN7+aN4RIQ044Qpa0qsfS+JIqVqVsYVIGcQEIvBBUNTBVAzQTvnzWa7CTDTiRtKkLWd8nY2Dqiu8eNatUNF1lxmimQD3hO5BK2NJShATqWqSOC/KkruUN0M4BvSCnyCcFwPo/md4AUE/4/6oGmqkwZd2PiyeiV0fbBZ+oVY1Y1TDWoXJzhPkcVFmkuhqMiyrLquJkwkyxsh9mugpa2c9lDdwEcLxpgWJsiL1VkQpDRopIMQxVRTkRWKWqYRquQ/7Mx12J5BpGZqkmSIZ9P98sNs+uZg71hCaRBBRZMtx6x3Fcc/Nr8ZEXfABXP/opAABa2Q8yBtFYwM74mBYiJ9akiqu/8iLy78lNeh9FBgwTZgpivapXQNN9sKvnwszWEGfrMO0Mbj7LmxYx8oYsN+tkBdRMYaarvNFtg2gZf4mloljmExeJQe2B0IpZc9FL2I51cvLdILUUrpJxNXyfaqZA1fBGMtyXjPNUPit0QM1WPxM60GwdacIGB1rM4OR5KskzE06moJrHQ9N9fFJUU6RqgmTr7Ofp9WE5LchKglIEuQBUDVsdVU2Ui3QeU9XANIy5BQCpXkWqpojNKrpECAE5RGccUnImtGuZo2SK0k5+/MQteP3N1+CGF30YVz7hEGLHAGlYPQ+mboDZOtKi7n0ScvnNEnWywgxRT3kT1SsIoOwH6T3FFs44VNMp2+G7OTPKdAarvo9W/o+9SsCohjVbrOoJkm0QdMO6JnvWsyogXuzsffYL+WmBSQvrF9mSk61LkIu2qGzU6OasZaNWZ/aseh/MvgXQzmF8Kxarrh+TMfyceiLMN0HU+asmvGEje/eTePuIAEcW1lhUTQUyNp96ej0wxrJgCp43ud6dRKBEKUwUm32I1RSLwPBIGk+XHaFIoFSo4zukXcwczBg+cs64TwlHTxzGdX94Dd79vBvx1MdegXWf0DhJ7ZzsRzSOC7RMV1ltUP1dLqu6sKlmaRfdBIsALELM3vSswkGdVeo9n6Bppqim57H33C/EHOnF1yK7T6RsdP1mDSC0PqHzCV0MOY5KyRKHsnCU8CrqehUmephujhBaUNP2DtDsnRaHo+FnwdaI1QTROLQBaD3nfmjeffksQzIms4J6ZRU2BTZhhzb7HCg7KCl7waMwXXITdBFYxIRuzmPysc+5VxO8hoE01qCuppyPIyolkQHVTb9OolKZukGyFWI1RaoY3KF1Uyw8Y4aFmBAScpi8IyCJpx0pnRGD7ErmKE8MRRo8cvthXPfJa/CbP/RBfN+jr8RGx4vSSahumJwL45rsxEPlxZkU2XNtVJ1ixL+OHBaeIWN04uc+5hggQENL+vifxmqwYo3KNXCNBCaOQioiuPB9V2yeRUQO9uMAvT6pyFmDRgARHAG1IzTWoq72oW4gjrKFqCF6b2LLnapQbWTsrUUb0Hou7KOgCpp/j2I8HFNmcjxZZSeo6imqSe905Q4yyiDHdzHSYzvvnzGOWytj1jR8vnMJk2TQ2Akq42CMA3zFp1M1Hc6ddXz6uQbR8Z1jreV16UKPNsMxZSkXp6fEMWFnUqhjdzIHBEVPpN5RYYxf/Uc34EkHLsd98y5vqKlYTk+1EY2boJ5MYKopS8AkFz4igOQIdxMsIuMkzT3jRK0tGL1wQ17T6F2ABVptGL5npZLQ9tpgYi2cUaTBPiMtIghkkELNBKx3QZiwb19RUTQYsZbgRw1p31c7VFYTfSwqt7opUDEmYcCu3zxrLUcjb0jEbetZDVEdnQMT+42reRPTajSe4hLvkzI0MA8crj/3XO6sDYx4oolNZfuc++Gwr3GIMSA6g+gcmmYfyNV5jbKV0DjAVoi2RhuBRcuLsNZGibBmRueAyIjV2oEiq3Am9Y7jnZ4du5I5ADGTJ4YA/aefvAa//qwb8KRHXo51yWnQcPC5AIedaiPamHgzmRpVU0vqpjjVRPp1IvEWIWLWJcaIaj3WFgEbHadzLnxE5zUdFXDW5vwPzTvQMOvKSe6H5B4kVTckFFwXlVNG+afzfe6E5jk0lcNKbaU4jsNaE7AqeRSNZMkNmTBlJtTnrBWIjOuLICmpHE7f51CYnDm4IqH6K5WGvXNmn5MkKaBHe+x8wNzzScHpyCFD7fgQciJTJUy3f+Iw9w6t3BH2Nw4RkbUBS6hsDdfUEsiDbJbtAtDKWi4kO+3eWSeQRSmjlkwS541QbWFjQiSCgpDslHYdc+ipkVLC0RO34E1/eA3+7XNuxHcfeAbWWp+lL8BSdOL49/vnHtPKorUJtSNUoc874HZ5kTpB/pt7BlBba7mC0v3zDqfmDKQ2zoozhvOcJ85gpeFNrBurdiwpjYR5R9kMbUhoA0s8RgrssOgC1tvA6omOITMHt7lvUuG8lYiNzmImueCrznLEsLXFZupxu9Y953ystQxqd99Gh5nkbS80AUtyNazhKk8TgfPU8eR8cM3VlrHEJNjBwhjK4BsLRmRfdGEIUSqZhV1IEDw4GCgUkUVKETERfOwTmAAggBm4iymrbLOOVbv75l1Gfwc4KcwS4K3JqDRRjClRTo+d0K5jDgAZG/cNN1+Ddz33RjzlMVdirQsZJKwNkdH8irzl++YeixCxWllMk0VnUlYRlEp1Z9YFgdwP/CN/b7S80eZdKFQfoLIBlTPYaEOWuozfZHPus5KPkZOfijY3siQPbNWJKZsvrTVoJBOPrXIJ3cQhKkNLktLMxIx3leTeotJ8wwecmvvM4KfmHrNF4EusoAsS8SatncHCW84u9AGLjvG4djqWecdAEHoClmAJE0lX1hPRGcnTaDmk3hoH6KlXZGYqZGkXe1V01qlaFQQCNsEZFkS1NdkAoKklSX4HnWXcqr8riuhTH9/z/Bvx9MdehW7ku4spCVBbb9Zbaz0irCB9cy0LTcovfWCKlOjF6qH6eEyKaJjy/1GSc9QcqlYflZQhMrNNKgNrYtbTGYEwZXRFBalWSaz4vQCfaADQEWA61qUrG+SSHAs1yqA2acAcbUxoNaOvizmVllUdfmYIMSOKJCQYGH6PGJy5DQZVSDByksVk0FHK8xxiyu0uPDP5wscsPIKilRgGWBvMoZrgkaQ0dsIiBBDEMz9aFzUgrHt+hpZD2OhCVgsNqZ9nyd5JLMgUKfN0dCbh7X/rREQ/QUSJiHaMuHb0BMOrXP/8G3H5wUN8lwZytpuTjDqgXzwAaKOkfMrkrvuIuaAe6o8aXAFeTEt9RhrfKfinESQPZ1iqWwFkzqgXZrgyZW460EtNzsXmVNCmslkfd87CVhbGGtjKwgq6RmVpU9sRKafd+ogMA+ojM6m+r6ToI3zasUXKVjb/aB+aiu8ete37as3pFXZtW+dC58eJ6tlUw7msnYEjEVLK2BC4oGJt5iEMGENhUXV+M3KJGDAsSXIXhoxy9PZbcK3AO52OztrJQUQXA3g2gNvP5HslBGiU5BVDbLXpnEUbE2oBMdBCMQD7q3wAPCVYSvAU4cnAgkGIVbllRjNoTERyFqI5cUKV+BqaymO9CvBiHcn6OjHcj7PKRAxAwAjnZpCL5EPCpErogqgvnce8tmytKi7k/OweiqdxNt8DJhXDYtaCoOJsf4ciA5BgyfarzL9YwwgfCppQ3gksMWTQxA3HoMJADQt5TmPku5vhbENDJAy1fG6aitXN/RNGFFlxNlv5GsP3swELph7adSH/888wzlL7V0vpZzatC1yPrOvxE4fx+pt3Ds9zNtWq3wQDu/3nM/nS+1/4IVx+kHOCkUiN7ojOYIoEH02/2EQFFhIGpk5FQyQ5ehgQAPx7dripzZ8w8RYT57HaWMy7KltiFN8KgHyHdfbG9VJRc58VnABgia/g1mxOrRlUWS7IY2mop82kshl5RFXDRvGczBB5w5sEbwmLYFCbiNpETCqDeeeySjd+jvafTzRBmLcsMBgNpbCGFcYFP4lovWOwah8zyoqGsxthDkV0WXE2I7pkPF1L/TrIGAIho1fanPaLDN4GcJUpZko2D684g2mtQolP6s+cPILX33wN3veCG3HFwZ2BLZwtxMMfBnBHSukvTuexHANJX3ExIx0SND2WF4wowcAC7BeCMYTW9xfyiWxUZ3QzKfZUDzgwNoUGA0wcow/yse6yybIN6o/A8Ei3iprBC1MJvpWac620H8DIjEHuR15QytvYM80oAj1v0FpOEvXlqNTMWZEQV6BeYgV8YSFo6+UzgD7YtUct6VFR1CmohXrK/qsZ1y9pd7t5mbgh2spW8x8TQJFNTykViC/GoC6yglcqK74g9svskxOptuxwvPWOwz1jyImxffoY01kBkgbws2CV6rS0DEhaGSqfAgYwUXx5sLATQiV6qZYgWHEu30nGMDiavG/MZkgZhtpJWImEEBO8oHHohvOxR3JXqaeOLmW8jNYxQvrmkPs0KLQTIFI/xMxAAPLGJCpgL7drW9oPSIg5T7u3+vDYNrfvFKEQWIoeuLntlENDesZgs2k5L7qx1QhSyca1BlvMO5uKDQmDuF4nJYpwBvCSKLWvdhkhZlX9MY7X9PgdR/A6QTrc6Ymh9C0Hkiai7wXwBAB6ahwE8AUiuiSl9LXTtasHjeqRekF1RKgM3yeMSOy5o8wc+ycuL1KGmMyhEYpuUYRGpNTf5hwjcfiEjPbhoxFUC97g6l8yoHw/KZE/VPdFGUoC5PALDYeJiS/SAXYQXJk/jj7KVDeUFXVwfF/WgMJQtBN20GZ/qUaPijLqM8QpF4o5yQGgEUMjgDCWGjistJ9DazSJSReYjJRnI5iYYIKsK0wWDr4w1Z43EeawFo3t4ZOOnzyCaz/+SnzwxTfhioNnDs/zLVerUkr/DcCj9G8i+jKAp6WU7t5pG33QH/XIIwAiFLGC0JoIZyy8jPBcKZFFsijKELWEZlgkiULtoGANZRxOMhxBCgFngJX/yQACYZP3pn4/BlAQyJ6tkD8KxI8qlwq20HRZFp2mB1DQeUuc3JShUjKggpiAVYpo+/J7Mlu1k6SvadD/AchWv2hgFBcLV8xJsprx18ceZPtTinn81Pqlc5xDRMhybXfXCLgd0IrJ3RDf7RTGB2DB5wiCbcWC79aTh/Hqj70CH37JTbjycYfEeNDD8+zETLvr/BxAf2IYw7AtivVkyMDaSoDRDJzp/RwTMeNki4yoUrVFjnBFjjptl6JcJF34YhE3QdkMoHV0k3nOpQ6e3/fdpk2h0DrGSuahc8NnoXjG+J62JJhu8ImtPq9JVBmELQCe+5jzNYq89dyO5IkYVzHTjpj69PPBRnNFQlE0FUg2J2wNxJqjcasJGudAgev9WerRF5VWXI9rVTvC0dtvwSv/0yvw4RfdgEMHLwfADg6jqtrybbWJzjpzpJQefyafN5AAMlVTYigiUsGh1a5muB1B2AOQQYdVDckAYcIYS3GougVbokY345wrIaHaGaSATJbgurmS5o0oGEOQHPY0UieMlVx0TmXN7ZZps5oJV+SYk4InnG6eJX02Q+0UqcJRcjMyiEHoOGOy7KOkpA6SqBSbqugfaXpvORcK7SPAFDm/JUUMEFeqpse5igGouIw1qgka62CJ0BEQEiGZkjk0rAU48td/gld8/Efwkef/Lq5+7KVIfoHkGhjjYAhnhEBy1pnjTEmvAUb0VRKQrz7VkoAUYGJA5WpYSfhvnMlvZ31XQr0RWsZICswQab6BJMgXg42ifSg3sUj9ASiCbkBFKVGmCL5nGt/1XnApQAmwI4ycop/0wAjlhky6oVwFsVBgkAdeUin5Y+AMyBSHjKqnROhPtxRC7l8ed9G3pH1yfNIpWstW86BoJuO5BCCZmBWo5jniNTY5XZgZEnCStWgTkFJvtm4cwaSAw//rT/HyT7waH33Oe3D1Y54OhAWACoicWWmIGMOqUMm2o93HHGXYcSqO/SheIaJeFUoRxnGdjKo4SwkQWExOxVQVCilkSZ+6xQC0TCF9uAHenHmTWscQmvqe9k03gp4c0nb0nFcefV+vIzdtCUQtTGUZgKEAf0uKliInC4LvT5jglzNIDJsxqBTNY0m/YheQUhz0i/vEmFQmJpDpmEkUoMJV3Ja1w7uRzoEyn5xWqURatI6RTmwQJjeSTCVqra5r9AARHFmkkZZoosfhv/4TvPwPfhQffc67cfVjny7zYQDjMqgGkYXBzk+PXcccSku9I3pBLTO+xEs8vDKrDrwD+0WpVikgAyKQJHcaDgmss5NzQ6uOtaAQ+BKc+IesZdMkwLA0drgRU+DXoiBr6lYjYwQgQvRyflE+ZJefHjHwa1HUFx1rCHnDjBl2zBglkTHDk01VKTlJ+0H0zxmcSkvgg7hvEah7SJ8li5DXi0ixX3glAODwl/+rMMZ7cPVjnlaoqyPjg/6Tttg/I9p1zKH3tv4FtfaYgZ7LG8Ph8N8cLv62w4Y0yclYkGFkdHI10BSLaC2SpmpSkeGkeFDG9tK8VLGAPp9bwMhIVBhbs7S2wWf1pUQkzJvQ2kEKLznuH7keXgeCPaW6vt5B9I6RgufP+i5D7oAI8C2SF5eeMbCW+2KcW94XV/V3ipGqV445jzsGwCZATylj+F5YQuzoyVs3PC4BgDDNlC/4RsAmyot+/5S81i//xGvwkeddj6sf8wP9upUILmNLHy21YWyiXcccSgmsl7JklA2eIgtHmZBbTh7Hy/6QnevKVTonRBbJgjcWMMCaJScboJ3z3aOeDtD2+GO8YINLqVxW82U5d7a//G57OR9L1YLxMtaUIKSQq7NFK2VkxgIzV3O8U6E2eg/4lplU4Xy6tr8LqOpYpjmqoWCbS/imzVdY5MrxIqXNc5hxhHvUyWhrQAAnkq0yDtVg/QoJ+ZHnvx9XX3QpEDq+UEDUXmUso6jxZ0a7mjlSkdxPCs8jVYM+/ZXP4mWffCM+/MLfw7P/7xdDc7dLjcGQhVGgM79g/TS0gG8Zk6qZZmmfywzkLxdSvdikLOUK30LucBJDgZZHKC7FhTVnQPKMwXMMw+mwZB36FtLomYqunhRuR/0MkfFns3l52fjK5xuTGSNlaW56ib5pnDHfF0iYMpux9VTZNIdVzndPAgiRXL0cnE0jA8Sfcug7DjEDmth72ckApsqwSqlgrJ3S7mQO9SQTYMnCOJFegXXYW04eyYxx6PE/CEDCGySMe+wdZjC4Ce/xooxBUnhKVQfKbxaOOnbWVRmKNGNBjS+nKfXOwagbyPenxvgZ6tsQKai+hGR7xhhvHD17jHxdTd4ZuVwQDXf07OIuE/XZZzpGRUYfOD/T4BmDORTgt0QWPumVL2XvthpjoumL1yS5gxERUgqAlmWQEyeCcjTDmdCuY44kTMF/8E8ygnRoLG758qfx8ptfjw+/6IM49PhnIol0UdwpTbLRsA8ObUgZNMCRhbMOphL8JrWYqDMLyJtCT4oADd+WxCefcsGUnlhntlSzr8Uhh1FsCi0ZOwglxCTKcxRxJbbiEJNTU8NN+GuUc11yKIup4EwNazXQEH1oyJJnoggR0WQvrqmTGLs66SL037NEMKbh3HqnjtrRPJY0mkcfgRgSj2+LUBRtM4nZKjOqti9tJtEWYhyaXXYKQLLrmANA9o4m8IlAkaX/8ZPHcM3HX42bXvJhXCWFS1R9bkPM+FYa5Ne3guw/KQP5OEbKZLDnDNQHObm6hJBiLmeWN24cBuApcft9OTKNZXISfKcb2YxUlSiWGg30GwcR+hRzhG9JGknL0QJbByuakZWD2+YtWQYWakCkllfb5DjXgEvTFxXS2oPMNNUA/UPnMXl+Hgde9mPU9NY8fwCMSbCJ4CIQxRHoI2CMqMjaLjZrCvrcnWJX7TrmWBZARwCO384Zgh988U24/OAhtCIMFWOqk+R8DpLjqFoNu1Yqw7KdNbJZe8bh5/P/5WZhLCtkRBGN2OWcjWH/DfXZihrWnss4S1xYGYGrY9YIWj2dvOBnKQNqfoX67TQjkcP5deP2oTM7eY7iZynsTv97/5z+WZAiowaWOAdGkVe0LDVRrxaVFiMBQUTCMBp5E7CdCBVLCcEkCGw4FjHBpbJYKnJtw3KP5CDNh6uHXBmjPHKPnzyMN9z8KrzvBTfi0ouuwkJPFpGsgDIHcu70Iqa8wdQTHBJyumYf8coLoCmcADJ4gW4aze1oJc9jIZl8ZdKSJv0AHDVqCDkpqmSMEt2jzIkrN39M/QbVvA8FXihJTyHNBSkZs2Se8TP8pp8+532ciKXPKZOx+ow8rsbL4+uFQDmfKfaIi+O1APr1YMRHgyYy9E6dzwjOPU9mKMDGKhmrY8wmdmcHx+5jjgiWBjHxEXzs9sN4k0CAXnLRVXwSFOe21ABCkJNEGWPuBQBApK8m+ivpphkXfC9BAbS0sWa+zTvOb9Z64G1IOZW2JE1FraVAfWVpkEWoyUv52abwQ6ounvrc6VAAFpRkCDmFVTew3q22attLW5op6EPIjNEKhE8sNjSrS/xTW0Lj+jz0ieBd9fktyAlV2j/t83j+dQ00+coToUkJcBZA5Ahp9TVK8ogxvWFC1TOlxK5xENKO4Xl2HXOoHhpTzxjveq4wRkx95iyQdWZAdFBNUBJ0jzJhSdWgcXWwZQ5bldSaZdcKWmHnGcpGc7MVf2ocRZrLFMvG4fwSD6dACsIg5eZWUrAGZYZSisdR5/WkKhlD2xq3WbanDLHoQkZG8aFnGhTzWo5lYQltlVB7QucYm2q+hOG3mtPxvHO9c0JM3IaPAIUIRwY+RJCYq2JMwIDJRUUseS0mNvwRZXie09EuZA5exGMnh4yRw6mQEEXPHgjs0eVRSTPxNKd7rJosiy4pN2XOl46aT64btUc+Ke8CAFtjIukLqiUX4R3gje6szc8CeEMvQzLp7bfDXacSeswI2k7uXzEexZryIQ4Yo2Ty8l4TY4IdgC4kRBLhEQKscfKciBCFSU8TsQMAJnFqbUyU1b1N2VwF6YZPBWOMDQZqACAkHD555LR92HXMATCKxBtv7lWpre5XVJiYOEnGICDBJYOUGAAsJnAsk+fF0Av0Mv29pwRjWaKxVI7oDMEINpUTONJKNlQVzIBRNHtRoXY0M1FPDoUYrSwN1CL+zmYm2cTQIyr7rowSYkJlkdUyQ2zurlzJYD3TGjIDRi3b608/2nT6VfKenlzj/mw1z6Uqprn/eiF38pwcd0ZnUH9DBOtr/+Ca03501zHH0ROH8bqbGdDtsguvGgh2Dr/RdE+eLZXQVgRzYy2AAAv+n8jAJYJB5NODtt5sS02s6IHfVM1i9UMusD4KyNxmdaRXd2igSi1TQ0pdnfuifTj9nC1Nn0Wv54/VxGX9H1/CdT7G/S+ZQaF8xn1fNofjdkvEEwWUYOR3TodVU7GOzxTrHUEDf3j56OMne3iel/z0c7edt13HHK/7g2tw/fNvxGWSE8yx+TwROQlK/if0k1aJ7d3HBCILRwwHWskdpHGM9Bfc8H4AIEt6NYuOaWxKVQtSb/YcXqKVxhdkZQa9uJZWK/XBqJVnZylOyykA2Srk49BKpYaG3iLW9x3o1TIAveNUGEDTlnvLmFimtpkzAJvuY2PzszJFI0zBOfn8HsBrC6hPUq1YNNgXRMCthVXzoY5b9aBIAd0AsJebS/YA6L2n6hEu16RxjGflDLGFyvApMk2bnXa6ecqNqA48jZYo/QNKy/wRavYtN2R5UVR1Xc3HTqJgFQyi9EVYcRTqwHZicSkpn7Ji1AhxiEISkvgGHmSfXTFHW80PMIQl0vkuaROKi1H0yd4AoI5MYMgcPUhFEUkB4DMnj+ANN78K1z9/Z4wB7ELmUNyhBLB3V3ZK6eRR5igRORpLiIayDVyxcFkqEkKiwmvea9t92yK59XTK3uXNfVRzoqKS6CUx5t/RjwGl5xa9o2zJc3SM+tmSObZSuQcGGxTPFudY2df4IPuZw1R2OCflc8o5L8eiz8jQQNTDfJbrC3AxH23fCHMEvZyDsZUVt2qnjAHsQuYYY1YNN3AftjCIGwJQqSEchMhheDncI+aF4mUabwY+6oeLsm08VN/ZHKMkazfakEPKm71khtwPfY7kiBS/89vbXD5UgpfoI6fpG7BF//Kluvd2j/u21RxoyOF43lV4lPOuTFfOe7+uxTMB2BRgySCJ/yJGrsWREnDkxOGMW3XlxYd2HFcFnF2s3LcAuA58qv5BSumndva9MgSBBhJ0wBSxRLoATDvLId1WQsqTcXwkk5XN0R/PWUqO2ws7jahF30IBv6O/D8opL6OURowwYsLi/eXPHfUBGD5v3Jfx+1v0Z1Nfcj+2GbtE8pplkb1SXTYuOfvy3AuOGHlf9KO4cHdzbsc4WGOzMLvly0fwGsGtulKQMhMNtYLt6GzBgf4ggB8G8OSU0oKIHnW67yipJCHSC+FIwmr0Z+jyJgbARSylDd0MlDeDbpLhAlFe/IIRNNxbilOWSUuayz7OpOOOS/i3JEOZXFO7zMMYb5DU9wPg7D4FLQB65hh70DZNWrH5tU/ybJ6PrZ7PfVAInU3IJUX+/qYxF+MtgSGSrUCkeSJ9GL7Zbv4Rh8w5opxWYAKnEBuLoyeO4VUfewVueslNuOpxhySyQRyAD/HYqjcBeEdKaQEAKaWv7/SLJWPYgjH0mB0zBgVJxg6F1AHyRiklaX5dF2ATc0iCkG+RuhaxzKjTdNDBSSJUptQSbY1cohA1I8qe7xFT5HRUpfGil5utTN/NuecFs4wow+cAkpAlCCIxLM9eLEHqxunDWnu9LDMtiVtQTC6dm00dSaP/i+fo/St0SBagCCQKOHz7Ebzi4z+Cm15yE65+3CHWBKRpPjVoqQl5TGeLOf4BgKuI6F8BmAP4yZTSbcs+OAaSLhljrPOToJGQSBsGK9ON5beUPGM0QWCoygxOiK7l1NluwUziPcP5SDZd7BjlI42kOcnG35SPTYalqzBNL903G2tzimkBYAD0VqCtKEfdjhBS9BnltwfPKNFTFDlEMvp0nPzR4alBxsBUDN+zKf+9aoC6YSYpgeHGKl65DksoaSai9JWiR7KEw39zGC+/+VrO5zl4BQs2MiAxFgDMILSDw+NsAUk7ABcAuAzA0wH8ByJ6YlqyymMgaVarxhfBM7hljSUQANpkTOS2VZ2IRSppapkRGLXDZwC4EtomZjd7sbDGZIgbU4W8gUCGsw4LoDgiQkI3RPQoacwU4/TW8UgUkE2B3XRPhdHGK9vVU0FRQwrG3wTfU+Sc6xhTjDAuAC728bOa89/y+qkQIeuyeklLVbuC8okPlGydyOCWk8fwsptfjw+/6AZc/TgtUyFqmTCIkc7sIILlWw8kDQBE9CYA/48ww58RUQRwAMBdO2l7S7MlGdaKIEesScVn9QIqzFSqT6d7njFIybDh3BhQ6nXqpMgfKXJZXxthpPBjCTxJ4hzI/2dzm6ghNFS7QKY/PUp1I6UemmegUm0xlkISD06jcZsQaZyiwAkpBxkOaSY+9VKUMQTTwwqpepaZn1W4EsKH6w2KamdEJdpCjdySSlW4PDmMxS13fAYv+8PX48Mv/D1WpcZqszax86edNbXqPwH4QQD/lYj+AYAawM6ApGn0B5nBayn1VhhCcdl0NV8cVY6lCMBueWxzW8JESHz8KxSO77IendE72gVs7WEKREMA2YmWoXYKILisUhXQPqToJeXG2QKsbdDXLS7lg823HSqitiH3pYwWEjpGLZHccyoA2jLEqD5rPD5BFVmKnpIv6WKT2s5SBgwtanJH0fF8+qt/xozxohtw6DueKZjGY6ajwa87yQY8W8zxAQAfIKIvAWgB/MgylWopJYwQ73rzK/9pxQDFlpDDf/Npfl+YY2yKPO1DVaqmCLiQ7zVG7yF6IR9D0GRDQLGByhNhCyxcZZoBuDKwebFHTD2ahcGrw5e2aifBlFapEoytxNJViNPRvWcwNmXyEspHLuQZeJoM5/dvIeGXUml+1rxxAC+7+fW46cU3MmYAhigjZavZhbNDLfysMEdKqQVw+nKeW5BGL6fi71KPZGcV4djJ43jlx1/Dz6ymvLBqI1dddBMVm0cXLPMtlyTOVjH9QRpC7iwzuS4xo5YbRSF9kryfduILUTqdXNnJ98c+DLW4JRYEOs6Mwr7kpFo6NvVtUIHUUprQx/0r5nozFSZ30zPWTS/5MK583CF0aRiIOXZaAv37D0s40Ig+RGDsXS3DI46dPJwLl7zw958Db2ueT4CDOpYhbgD9sY2e+UrPLcp3SyialARdY2u7fCLTX0wV2qdY6L7ex9BrDWwffbtNmsOOvzvwFZVm8dICOBobwNYkVXlSuemFGQZSfjS2koozMj+ff5VPjtanFG2XXnQIrU85r18/XjqLI/Vib2c3TYB2qs08FIgupIQ3nO1e7NHDht6Oz6eUnrbV27uOOe79HxuDU0IT6TVn+Po/fxd++ejb8PNX/Aqufep1MAAe9879OPnP1gZ180ppG4sjIiBtyiYr0TFuPXEYb/3Uq/BbP/TvcclFV+U2csQswPfF/tdNNFAcpF2NkP3MVw7jJz71avz6s27AUx97JX9+B0u0XdRHSZ/76lH81J++Gr/6j27A06R9/e64KOY4Erg/U7ce0613HMFbPnkN3vkcTkQbJ0cpjds1hD7yWZZpWSDj0ds5n+e9z//3eMbBQzj42/tw+1tODbSGHJNlSoglGpwmCcAF+1e2ZY5dp1Yl9LA8fVQthz+/7wvvwr869ja87YpfwauefB26gLyarWeEbmDzRsqOcPRM58OwIKYPEbd99Qj+xaevxduvej8uPucSfPXUYmkf+80mfy/Re8raF8qEX7zzGP7lkWvx81dcj4vPuQR3rrVnPD/bJUH9xZ3H8K+Pvw4/e/n1eNw5l+Dr6+3S75aoJBqNvNU4yvH8+deO4RcO8/xcuO/pOHn/fNPncnRzgSii4fklnpcqTxqSBgC3njyC6yQ1+gcecxUWUu9xMQ7tInblGAimQOwdx4kexugjO2GMa773nw6K3AOAF0W3lO46oaXkVsCysoSwj8Dnv3oEv3TstfiZy6/HE867FPfNu6WADCVlS+wOrOt/edcx/MZn3oAfv+y9+I5zL8V9c3/a74yfsxXFCPzVXcfxG3/2Bvz4Je/FE867FA8slrc/sPyO+r1VemtEwpfuOo7f+Mwb8GOXvBcX7X867t4YMZ5BgSaCnBylsD25JHWIGaOqPLk+e8cRvOWP+ER62oVXwRfM0PnCoSvfCYT+gpoXm2s/BuyMQXYdcwC9OS6BGeX9f94zxquffN3So3ycgaeMoa8vYwwvTPiFO4/il4+9Dj992fV40iMuz4lRy7L7xlSCG5SCt9xof3XXcfzWbW/EW5/+HvzDC56xo7ifsp3TxR0qY7z16e/Bdx3Yvv2h+2T55waMkYD/fveteOfn3ojrnvpuPPG8SzHr+kZy1mBEzhpEMHA2ZfCEkKTgUIiSz8zWFmcYZ+y2rxzFWz/1Kvzb5/QoM2dKec+IynZWPeR/VzQoPwbg/V/s7xivecp1COAjOo2k3uBOUBB/ltfFiT/RRsDCwMaEv/jaYfzSkdfi/7zq/fieRz6DK5JGLiw/zsEG+v+H+d6yQZZI5S/ddRy/fdsb8VOXXY/vfdTlg75tZ4XaqWP5L79+HL952xvwtiuux/dJ+9sx01b7bnxSaDt/dddxvPNzzNjf/cjLN31vnAO/7NTYDvHxc19lxnjncxiwD+DPAz3rOltEAcg/mk247O6XUlHcaBvadczBSNqsH73vC+/CLx55G37h0K/gtU95M1LigI1sdSzIlQ7SJXcOZyUBCsin0vETt+Bf3HItfv1ZN+Apj71ykD46huEElm+swWlR5KIDfAf4N599A37p6g/g+x9zRd+/Lbhiu7zxZYv9ha8exa8efz3+9TM/gKc+5sql31saVTYaiIZQlXMakfDFO4/ht257I37hyvfhex91BcY0vsMQ8TyPU2v5tR6CVS/pn73jCP7ZH12Df/dcxgzI/TvN2uY7CxXZlNIusDPvOLALmQPgMb7vC7+Dtx/+GfzLQ+/A6576Zn5DjmlWt4bfqexycITi6sFNyJ3m1pNH8OOf+hG867kssUqmUTxXAANM12XaSvnMHloUuO0rR/CLR6/Fbz/7g7jkwqvks5tPu+3mYDv67B1H8PO3/Ch+57m9xAW2UpSYlqmH5Uldjvm2rxzBLx99LX79WTfgaRdeue3Yx7n3YyYgjC7+RLj1jsN48x9dg/e84EZcIZgB40foMyuNVyt4QC1dwNCXo/Tez79zm5lg2nXMQQS85wu/g184/DP4xavfgTf+wFsAIJ8mGaJlLF0KxIxBe8Xv+pVjJ47gTZ98Fa5/wYdw+cFDmeH4OUCyJuus5aY4HXPo37eePIKf/NSr8Z7n3YhnHFzOGFt9fyd0/ORh/B9/fA3e+4IbcbmCUZyGuO9LrGqjQUVw///5n7wa7y4k+unGrr+rRN9uIx87cRhvuvlVeP8LPjTEDCj7ofds9Gur3y9HMp5XIuDdn38nfuHTP7O5wyPadczxXhnYLz7zHXiTMAbQT4IukqHhwjqzeZKW0VHJOf7Aiz6UJRbQVx8VY/BmFWo7kVw86/iJw3jzJ1+F972wX/glH3vQtGxjfTM0vrsdO3EY16ngKNvfavwDI8Tml8vNS9TPv+Z8b+pPsb5KCnwxeOwWk6mM8cvPfAd+Dj+9RaeZdh1z/LwMrGSMkuJAWg0nXmmru+zRExxy8nvLFoZoYOHg4iln1HUcKwDFToeCcQaB3JmOnmAkv6X93yFtZ8UpBceZghUAmzfseIzbzn9uZAnwwxL1c9n8lYzxph94y8OPObZjDGDrTXW6zXb0xGG85uOvxA3FwozXflMbZyDqd7Tw3wRp/7/Z9s9IcPxtHHVF+6eb/636uBNB8u7Pv/O0gnVMu445djqwM6FyY11x8aGdRjQ/qPYfyozxUGj/72L+HwxjAA/u9H5Y0cNpY+21v5keLGMA3+bMsdsXfq/97embYQxgt0XlEt0FYB07Tan99qUD2Juj7Ujn5ztSSo/c6kO7ijkAgIg+t12Y8R7tzdHpaKfz822tVu3RHm1He8yxR3u0Be1G5vjds92BXUB7c7Q97Wh+dt2dY4/26FtFu/Hk2KM9+pbQHnPs0R5tQbuSOYjo7UR0BxF9UX6ef7b79FAgInouEf2/RPQ/iej0MdnfhkREXyai/yb75nPbfnY33jmI6O0A1lJKv362+/JQISKyAP4HgB8CcBLAbQBellL672e1Yw8xIqIvA3haSum0TtJdeXLs0VK6BMD/TCn9L4Fb/Si4etYePUjazczxZiL6SyL6ABGdf7Y78xCgiwCcKP4+Ka/t0ZASgD8mos9LYaQt6SHLHET0X4joS0t+fhjAuwH8PQBPAfBVAP/mbPZ1j3YVXZlSeiqA5wG4joi2jHh8yOZzbFf8piQiuh7AJ/6Ou7Mb6A4AFxd/H5TX9qiglNId8v/Xieg/gtXRw8s++5A9ObYjInps8ec/AfCls9WXhxDdBuDvE9ETiKgG8FIAHzvLfXpIERGtEtF+/R3As7HN3nnInhynoV8loqeA9ccvA3vY6yklT0RvBvBH4BT3D6SU/uosd+uhRo8G8B8FW8AB+HBK6ZNbfXhXmnL3aI++FbQr1ao92qNvBe0xxx7t0Ra0xxx7tEdb0B5z7NEebUF7zLFHe7QF7THHw4SI6GIi+msiukD+Pl/+fvxZ7tqupT3meJhQSukEOKzmHfLSOwD8bkrpy2etU7uc9vwcDyMiogrA5wF8AMDrADwlpdSd3V7tXtqtHvI9WkIppY6I/jmATwJ49h5jfHO0p1Y9/Oh54Ejl7znbHdnttMccDyOSeLMfAnAZgB8bBWju0RnSHnM8TIg4mu7dAN6aUrodwK8B2Esj/iZojzkePvQ6ALenlD4lf/87AN9FRFefxT7tatqzVu3RHm1BeyfHHu3RFrTHHHu0R1vQHnPs0R5tQXvMsUd7tAXtMcce7dEWtMcce7RHW9Aec+zRHm1B/z+1GCXrsBdN1gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cwsrc = [mp.Source(mp.ContinuousSource(frequency=fcen), component=mp.Ez, size=source_size, center=source_center)]\n",
    "\n",
    "sim = mp.Simulation(\n",
    "    cell_size=mp.Vector3(Sx, 15),\n",
    "    boundary_layers=pml_layers,\n",
    "    geometry=geometry,\n",
    "    sources=cwsrc,\n",
    "    default_material=Air,\n",
    "    resolution=resolution,\n",
    ")\n",
    "\n",
    "sim.run(until=500)\n",
    "%matplotlib inline\n",
    "sim.plot2D(fields=mp.Ez)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "12a9a63d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "opt.plot2D(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "33034f2a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}